Inbesondere die Behandlung von zustandsbeschränkten Optimalsteuerproblemen mit partiellen Differentialgleichungen ist dabei von erhöhtem Interesse, da Lagrangesche Multiplikatoren bezüglich dieser Ungleichungsnebenbedingungen im allgemeinen nur Maße sind. Die Entwicklung und Untersuchung von effektiven Diskretisierungsstrategien und Optimierungsalgorithmen stellt somit eine große Herausforderung dar. Entscheidend ist dabei die Verknüpfung von Aspekten der nichtlinearen Optimierung und der Numerik partieller Differentialgleichungen. Ein anderer wichtiger Punkt ist aber auch die Analysis der zugrundeliegenden partiellen Differentialgleichung, also Aussagen über deren Lösbarkeit oder die Regularität. Erst mit Hilfe solcher Resultate können zum Beipiel Zustandsbeschränkungen korrekt formuliert werden oder a priori Fehlerabschätzungen für Diskretisierungsstrategien bewiesen werden.
Bei der Lösung nichtlinearer Optimierungsprobleme entstehen neue mathematische Herausforderungen, wenn die zugrunde liegenden Daten nicht differenzierbar oder zufallsbehaftet sind. Dies trifft insbesondere auf Probleme mit Gleichgewichtsrestriktionen (MPECs) oder auf die stochastische Optimierung zu, die beide von großer Bedeutung bei der Modellierung technologischer und wirtschaftlicher Prozesse sind. Beispiele sind etwa Gleichgewichte in Strommärkten oder die Kraftwerkseinsatzplanung unter unsicheren Parametern. In solchen Fällen treffen klassische Resultate zu Struktur, Stabilität und Numerik nicht mehr zu und müssen völlig neu erarbeitet werden.
Publikationen
Monografien

M. Hintermüller, T. Keil, Chapter 3: Optimal Control of Geometric Partial Differential Equations, in: Geometric Partial Differential Equations: Part 2, A. Bonito, R.H. Nochetto, eds., 22 of Handbook of Numerical Analysis, Elsevier, 2021, pp. 213270, (Chapter Published), DOI 10.1016/bs.hna.2020.10.003 .

M. Hintermüller, M. Hinze, J. Sokołowski, S. Ulbrich, eds., Special issue to honour Guenter Leugering on his 65th birthday, 1 of Control & Cybernetics, Systems Research Institute, Polish Academy of Sciences, Warsaw, 2019, (Collection Published).

M. Hintermüller, J.F. Rodrigues, eds., Topics in Applied Analysis and Optimisation  Partial Differential Equations, Stochastic and Numerical Analysis, CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, 396 pages, (Collection Published).

R. Henrion, Chapter 2: Calmness as a Constraint Qualification for MStationarity Conditions in MPECs, in: Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, D. Aussel, C.S. Lalitha, eds., Forum for Interdisciplinary Mathematics, Springer, Singapore, 2018, pp. 2141, (Chapter Published), DOI 10.1007/9789811047749 .

M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, Chapter 13: Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, 2017, pp. 305353, (Chapter Published), DOI 10.1007/9783319566023 .

M. Hintermüller, D. Wegner, Distributed and Boundary Control Problems for the Semidiscrete CahnHilliard/NavierStokes System with Nonsmooth GinzburgLandau Energies, in: Topological Optimization and Optimal Transport in the Applied Sciences, M. Bergounioux, E. Oudet, M. Rumpf, G. Carlier, Th. Champion, F. Santambrogio, eds., 17 of Radon Series on Computational and Applied Mathematics, De Gruyter, Berlin, 2017, pp. 4063, (Chapter Published).

P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, 22 of Springer INdAM Series, Springer International Publishing AG, Cham, 2017, xii+571 pages, (Collection Published).
Abstract
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; wellposedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a selfcontained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs. 
F.J. Aragón Artacho, R. Henrion, M.A. LópezCerdá, C. Sagastizábal, J.M. Borwein, eds., Special Issue: Advances in Monotone Operators Theory and Optimization, 25, issues 3 and 4, of SetValued and Variational Analysis, Springer International Publishing AG, Cham, 2017, 396 pages, (Collection Published).

D. Hömberg, G. Hu, eds., Issue on the workshop ``Electromagnetics  Modelling, Simulation, Control and Industrial Applications'', 8, no. 3 of Discrete Contin. Dyn. Syst. Ser. S, American Institute of Mathematical Sciences, Springfield, 2015, 259 pages, (Collection Published).

P. Colli, G. Gilardi, D. Hömberg, E. Rocca, eds., Special Issue dedicated to Jürgen Sprekels on the Occasion of his 65th Birthday, 35, no. 6 of Discrete Contin. Dyn. Syst. Ser. A, American Institute of Mathematical Sciences, Springfield, 2015, 472 pages, (Collection Published).

P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON  Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

A. Mielke, Chapter 21: Dissipative Quantum Mechanics Using GENERIC, in: Recent Trends in Dynamical Systems  Proceedings of a Conference in Honor of Jürgen Scheurle, A. Johann, H.P. Kruse, F. Rupp, S. Schmitz, eds., 35 of Springer Proceedings in Mathematics & Statistics, Springer, Basel et al., 2013, pp. 555585, (Chapter Published).
Abstract
Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for NonEquilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradientflow contribution, which satisfy a particular noninteraction condition. One of our models couples a quantum system to a finite number of heat baths each of which is described by a timedependent temperature. The dissipation mechanism is modeled via the canonical correlation operator, which is the inverse of the KuboMori metric for density matrices and which is strongly linked to the von Neumann entropy for quantum systems. Thus, one recovers the dissipative doublebracket operators of the Lindblad equations but encounters a correction term for the consistent coupling to the dissipative dynamics. For the finitedimensional and isothermal case we provide a general existence result and discuss sufficient conditions that guarantee that all solutions converge to the unique thermal equilibrium state. Finally, we compare of our gradient flow formulation for quantum systems with the Wasserstein gradient flow formulation for the FokkerPlanck equation and the entropy gradient flow formulation for reversible Markov chains. 
D. Hömberg, F. Tröltzsch, eds., System Modeling and Optimization, 25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 1216, 2011, 391 of IFIP Advances in Information and Communication Technology, Springer, Heidelberg [et al.], 2013, 568 pages, (Collection Published).

K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Coupled Systems of Partial Differential Equations, 158 of Internat. Series Numer. Math., Birkhäuser, Basel et al., 2009, 345 pages, (Collection Published).

B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279299, (Chapter Published).

R. Henrion, A. Kruger, J. Outrata, eds., Special Issue on: Variational Analysis and Generalised Differentiation, 16 of SetValued Analysis, Springer, Heidelberg, 2008, xii+231 pages, (Collection Published).

K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Control of Coupled Partial Differential Equations, 155 of Internat. Series Numer. Math., Birkhäuser, Berlin, 2007, 382 pages, (Collection Published).

P. Neittaanmäki, D. Tiba, J. Sprekels, Optimization of Elliptic Systems: Theory and Applications, Springer Monographs in Mathematics, Springer, New York, 2006, xvi+514 pages, (Monograph Published).

K.H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Complex Structures, 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, 289 pages, (Monograph Published).
Artikel in Referierten Journalen

P. Colli, A. Signori, J. Sprekels, Secondorder analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis, ESAIM. Control, Optimisation and Calculus of Variations, 27 (2021), pp. 73/173/46 (Published online on 13.07.2021), DOI 10.1051/cocv/2021072 .
Abstract
This paper concerns a distributed optimal control problem for a tumor growth model of CahnHilliard type including chemotaxis with possibly singular anpotentials, where the control and state variables are nonlinearly coupled. First, we discuss the weak wellposedness of the system under very general assumptions for the potentials, which may be singular and nonsmooth. Then, we establish the strong wellposedness of the system in a reduced setting, which however admits the logarithmic potential: this analysis will lay the foundation for the study of the corresponding optimal control problem. Concerning the optimization problem, we address the existence of minimizers and establish both firstorder necessary and secondorder sufficient conditions for optimality. The mathematically challenging secondorder analysis is completely performed here, after showing that the solution mapping is twice continuously differentiable between suitable Banach spaces via the implicit function theorem. Then, we completely identify the secondorder Fréchet derivative of the controltostate operator and carry out a thorough and detailed investigation about the related properties. 
J. Sprekels, F. Tröltzsch, Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth, ESAIM. Control, Optimisation and Calculus of Variations, 27 (2021), pp. S26/1S26/27, DOI 10.1051/cocv/2020088 .
Abstract
In this paper, we study an optimal control problem for a nonlinear system of reactiondiffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally introduced in [13]. The model takes the effect of chemotaxis into account but neglects velocity contributions. The unknown quantities of the governing state equations are the chemical potential, the (normalized) tumor fraction, and the nutrient extracellular water concentration. The equation governing the evolution of the tumor fraction is dominated by the variational derivative of a doublewell potential which may be of singular (e.g., logarithmic) type. In contrast to the recent paper [10] on the same system, we consider in this paper sparsity effects, which means that the cost functional contains a nondifferentiable (but convex) contribution like the L^{1}norm. For such problems, we derive firstorder necessary optimality conditions and conditions for directional sparsity, both with respect to space and time, where the latter case is of particular interest for practical medical applications in which the control variables are given by the administration of cytotoxic drugs or by the supply of nutrients. In addition to these results, we prove that the corresponding controltostate operator is twice continuously differentiable between suitable Banach spaces, using the implicit function theorem. This result, which complements and sharpens a differentiability result derived in [10], constitutes a prerequisite for a future derivation of secondorder sufficient optimality conditions. 
C. Geiersbach, E. LoayzaRomero, K. Welker, Stochastic approximation for optimization in shape spaces, SIAM Journal on Optimization, 31 (2021), pp. 348376, DOI 10.1137/20M1316111 .

C. Geiersbach, T. Scarinci, Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces, Computational Optimization and Applications. An International Journal, 78 (2021), pp. 705740, DOI 10.1007/s1058902000259y .

M. Hintermüller, S. Rösel, Duality results and regularization schemes for PrandtlReuss perfect plasticity, ESAIM. Control, Optimisation and Calculus of Variations, 27 (2021), pp. S1/1S1/32, DOI 10.1051/cocv/2018004 .
Abstract
We consider the timediscretized problem of the quasistatic evolution problem in perfect plasticity posed in a nonreflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primaldual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a welldefined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be wellsuited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinitedimensional setting based on the semismooth Newton method is proposed. 
C. Geiersbach, W. Wollner, A stochastic gradient method with mesh refinement for PDEconstrained optimization under uncertainty, SIAM Journal on Scientific Computing, 42 (2020), pp. A2750A2772, DOI 10.1137/19M1263297 .

M.H. Farshbaf Shaker, M. Gugat, H. Heitsch, R. Henrion, Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints, SIAM Journal on Control and Optimization, 58 (2020), pp. 22882311, DOI 10.1137/19M1269944 .
Abstract
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented. 
M.S. Aronna, J.F. Bonnans, A. Kröner, Stateconstrained controlaffine parabolic problems I: First and second order necessary optimality conditions, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 29 (2021), pp. 383408 (published online on 17.10.2020), DOI 10.1007/s11228020005602 .
Abstract
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear controlstate terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasiradial critical directions. 
M.J. Cánovas, M.J. Gisbert, R. Henrion, J. Parra, Lipschitz lower semicontinuity moduli for linear inequality systems, Journal of Mathematical Analysis and Applications, 2 (2020), pp. 124313/1124313/21, DOI 10.1016/j.jmaa.2020.124313 .
Abstract
The paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, righthand side and lefthand side perturbations. Inspired by [14], we introduce the Lipschitz lower semicontinuitystar as an intermediate notion between the Lipschitz lower semicontinuity and the wellknown Aubin property. We provide explicit pointbased formulae for the moduli (best constants) of all three Lipschitz properties in all three perturbation settings. 
A. Ivanova, P. Dvurechensky, A. Gasnikov, Composite optimization for the resource allocation problem, Optimization Methods & Software, published online on 12.02.2020, urlhttps://doi.org/10.1080/10556788.2020.1712599, DOI 10.1080/10556788.2020.1712599 .
Abstract
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium. 
F. Auricchio, E. Bonetti, M. Carraturo, D. Hömberg, A. Reali, E. Rocca, A phasefieldbased gradedmaterial topology optimization with stress constraint, Mathematical Models & Methods in Applied Sciences, 30 (2020), pp. 14611483, DOI 10.1142/S0218202520500281 .
Abstract
In this paper a phasefield approach for structural topology optimization for a 3Dprinting process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a twodimensional cantilever beam problem. Finally, a possible workflow to obtain a 3Dprinted object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer. 
M. Brokate, Newton and Bouligand derivatives of the scalar play and stop operator, Mathematical Modelling of Natural Phenomena, 15 (2020), pp. 51/151/34, DOI 10.1051/mmnp/2020013 .

P. Colli, M.H. Farshbaf Shaker, K. Shirakawa, N. Yamazaki, Optimal control for shape memory alloys of the onedimensional Frémond model, Numerical Functional Analysis and Optimization. An International Journal, 41 (2020), pp. 14211471, DOI 10.1080/01630563.2020.1774892 .
Abstract
In this paper, we consider optimal control problems for the onedimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudopotential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems. 
D. Kamzolov, P. Dvurechensky, A. Gasnikov, Universal intermediate gradient method for convex problems with inexact oracle, Optimization Methods & Software, published online on 17.01.2020, urlhttps://doi.org/10.1080/10556788.2019.1711079, DOI 10.1080/10556788.2019.1711079 .

Y. Nesterov , A. Gasnikov, S. Guminov, P. Dvurechensky, Primaldual accelerated gradient methods with smalldimensional relaxation oracle, Optimization Methods & Software, published online on 02.03.2020, urlhttps://doi.org/10.1080/10556788.2020.1731747, DOI 10.1080/10556788.2020.1731747 .

C. Rautenberg, M. Hintermüller, A. Alphonse, Stability of the solution set of quasivariational inequalities and optimal control, SIAM Journal on Control and Optimization, 58 (2020), pp. 35083532, DOI 10.1137/19M1250327 .

M.S. Aronna, J.F. Bonnans, A. Kröner, Optimal control of PDEs in a complex space setting: Application to the Schrödinger equation, SIAM Journal on Control and Optimization, 57 (2019), pp. 13901412, DOI 10.1137/17M1117653 .

L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, SIAM Journal on Applied Mathematics, 79 (2019), pp. 257283, DOI 10.1137/18M1179183 .
Abstract
A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
H. Antil, C.N. Rautenberg, Sobolev spaces with nonMuckenhoupt weights, fractional elliptic operators, and applications, SIAM Journal on Mathematical Analysis, 51 (2019), pp. 24792503, DOI 10.1137/18M1224970 .
Abstract
We propose a new variational model in weighted Sobolev spaces with nonstandard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply. For special cases of the weights, the resulting variational problem is known to be equivalent to the fractional Poisson problem. The trace space for the weighted Sobolev space is identified to be embedded in a weighted L2 space. We propose a finite element scheme to solve the EulerLagrange equations, and for the image denoising application we propose an algorithm to identify the unknown weights. The approach is illustrated on several test problems and it yields better results when compared to the existing total variation techniques. 
P. Colli, G. Gilardi, J. Sprekels, A distributed control problem for a fractional tumor growth model, Mathematics  Open Access Journal, 7 (2019), pp. 792/1792/32, DOI 10.3390/math7090792 .
Abstract
In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a CahnHilliard type phase field system modeling tumor growth that goes back to HawkinsDaarud et al. (Int. J. Numer. Math. Biomed. Eng. 28 (2012), 324.) The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in the recent work Adv. Math. Sci. Appl. 28 (2019), 343375 by the present authors. In our analysis, we show the Fréchet differentiability of the associated controltostate operator, establish the existence of solutions to the associated adjoint system, and derive the firstorder necessary conditions of optimality for a cost functional of tracking type. 
P. Colli, G. Gilardi, J. Sprekels, Deep quench approximation and optimal control of general CahnHilliard systems with fractional operators and double obstacle potentials, Discrete and Continuous Dynamical Systems  Series S, 14 (2021), pp. 243271 (published online on 21.12.2019), DOI 10.3934/dcdss.2020213 .
Abstract
In the recent paper ”Wellposedness and regularity for a generalized fractional CahnHilliard system”, the same authors derived general wellposedness and regularity results for a rather general system of evolutionary operator equations having the structure of a CahnHilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated doublewell potentials driving the phase separation process modeled by the CahnHilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper ”Optimal distributed control of a generalized fractional CahnHilliard system” (Appl. Math. Optim. (2018), https://doi.org/10.1007/s0024501895407) by the same authors, an analysis of distributed optimal control problems was performed for such evolutionary systems, where only the differentiable case of certain polynomial and logarithmic doublewell potentials could be admitted. Results concerning existence of optimizers and firstorder necessary optimality conditions were derived, where more restrictive conditions on the operators A and B had to be assumed in order to be able to show differentiability properties for the associated controltostate operator. In the present paper, we complement these results by studying a distributed control problem for such evolutionary systems in the case of nondifferentiable nonlinearities of double obstacle type. For such nonlinearities, it is well known that the standard constraint qualifications cannot be applied to construct appropriate Lagrange multipliers. To overcome this difficulty, we follow here the socalled ”deep quench” method. This technique, in which the nondifferentiable double obstacle nonlinearity is approximated by differentiable logarithmic nonlinearities, was first developed by P. Colli, M.H. FarshbafShaker and J. Sprekels in the paper ”A deep quench approach to the optimal control of an AllenCahn equation with dynamic boundary conditions and double obstacles” (Appl. Math. Optim. 71 (2015), pp. 124) and has proved to be a powerful tool in a number of optimal control problems with double obstacle potentials in the framework of systems of CahnHilliard type. We first give a general convergence analysis of the deep quench approximation that includes an error estimate and then demonstrate that its use leads in the double obstacle case to appropriate firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint state system. 
P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective CahnHilliard system with double obstacles and dynamic boundary conditions: A `deep quench' approach, Journal of Convex Analysis, 26 (2019), pp. 485514.
Abstract
In this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents a difficulty for the analysis. In contrast to the previous paper Optimal velocity control of a viscous CahnHilliard system with convection and dynamic boundary conditions by the same authors, the bulk and surface free energies are of double obstacle type, which renders the state constraint nondifferentiable. It is well known that for such cases standard constraint qualifications are not satisfied so that standard methods do not apply to yield the existence of Lagrange multipliers. In this paper, we overcome this difficulty by taking advantage of results established in the quoted paper for logarithmic nonlinearities, using a socalled `deep quench approximation'. We derive results concerning the existence of optimal controls and the firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint system. 
P. Colli, G. Gilardi, J. Sprekels, Recent results on wellposedness and optimal control for a class of generalized fractional CahnHilliard systems, Control and Cybernetics, 48 (2019), pp. 153197.

P. Colli, A. Signori, J. Sprekels, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 83 (2021), pp. 20172049 (published online on 21.10.2019), and 2021 Correction to: Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials (https://doi.org/10.1007/s0024502109771x), DOI 10.1007/s00245019096186 .
Abstract
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design the dispensation of some drugs to the patient. The cost functional is of tracking type, whereas the potential setting has been kept quite general in order to allow regular and singular potentials to be considered. In this direction, some relaxation terms have been introduced in the system. We show the wellposedness of the state system, the Fréchet differentiability of the controltostate operator in a suitable functional analytic framework, and, lastly, we characterize the firstorder necessary conditions of optimality in terms of a variational inequality involving the adjoint variables. 
S.P. Frigeri, C.G. Gal, M. Grasselli, J. Sprekels, Strong solutions to nonlocal 2D CahnHilliardNavierStokes systems with nonconstant viscosity, degenerate mobility and singular potential, Nonlinearity, 32 (2019), pp. 678727, DOI 10.1088/13616544/aaedd0 .
Abstract
We consider a nonlinear system which consists of the incompressible NavierStokes equations coupled with a convective nonlocal CahnHilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We suppose that the viscosity depends smoothly on the order parameter as well as the mobility. Moreover, we assume that the mobility is degenerate at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with noslip boundary condition for the (average) velocity and homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the twodimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weakstrong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal CahnHilliard equation, with a given velocity field, in the three dimensional case as well. 
G. Gilardi, J. Sprekels, Asymptotic limits and optimal control for the CahnHilliard system with convection and dynamic boundary conditions, Nonlinear Analysis. An International Mathematical Journal, 178 (2019), pp. 131, DOI 10.1016/j.na.2018.07.007 .
Abstract
In this paper, we study initialboundary value problems for the CahnHilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding chemical potential. While recent works addressed the case of viscous CahnHilliard systems, the `pure' nonviscous case is investigated here. In its first part, the paper deals with the asymptotic behavior of the solutions as time approaches infinity. It is shown that the $omega$limit of any trajectory can be characterized in terms of stationary solutions, provided the initial data are sufficiently smooth. The second part of the paper deals with the optimal control of the system by the fluid velocity. Results concerning existence and firstorder necessary optimality conditions are proved. Here, we have to restrict ourselves to the case of everywhere defined smooth potentials. In both parts of the paper, we start from corresponding known results for the viscous case, derive sufficiently strong estimates that are uniform with respect to the (positive) viscosity parameter, and then let the viscosity tend to zero to establish the sought results for the nonviscous case. 
P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Vietnam Journal of Mathematics, 47 (2019), pp. 793812, DOI 10.1007/s10013019003555 .
Abstract
In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heatermagnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heatermagnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solidliquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solidliquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization. 
J. Sprekels, H. Wu, Optimal distributed control of a CahnHilliardDarcy system with mass sources, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 83 (2021), pp. 489530 (published online on 24.01.2019), DOI 10.1007/s00245019095554 .
Abstract
In this paper, we study an optimal control problem for a twodimensional CahnHilliardDarcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the controltostate operator is Fréchet differentiable between suitable Banach spaces and derive the firstorder necessary optimality conditions in terms of the adjoint variables and the usual variational inequality. 
M. Hintermüller, N. Strogies, Identification of the friction function in a semilinear system for gas transport through a network, Optimization Methods & Software, 35 (2020), pp. 576617 (published online on 10.12.2019), DOI 10.1080/10556788.2019.1692206 .

D. Hömberg, K. Krumbiegel, N. Togobytska, Optimal control of multiphase steel production, Journal of Mathematics in Industry, 9 (2019), pp. 132, DOI 10.1186/s133620190063x .
Abstract
An optimal control problem for the production of multiphase steel is investigated, where the state equations are a semilinear heat equation and an ordinary differential equation, which describes the evolution of the ferrite phase fraction. The optimal control problem is analyzed and the firstorder necessary and secondorder sufficient optimality conditions are derived. For the numerical solution of the control problem reduced sequential quadratic programming (rSQP) method with a primaldual active set strategy (PDAS) was applied. The numerical results were presented for the optimal control of a cooling line for production of hot rolled MoMn dual phase steel. 
R. Lasarzik, Approximation and optimal control of dissipative solutions to the EricksenLeslie system, Numerical Functional Analysis and Optimization. An International Journal, 40 (2019), pp. 17211767, DOI 10.1080/01630563.2019.1632895 .
Abstract
We analyze the EricksenLeslie system equipped with the OseenFrank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the earlier introduced measurevalued solutions. In this article, we argue that dissipative solutions can be numerically approximated by a relative simple scheme, which fulfills the normrestriction on the director in every step. We introduce a semidiscrete scheme and derive an approximated version of the relativeenergy inequality for solutions of this scheme. Passing to the limit in the semidiscretization, we attain dissipative solutions. Additionally, we introduce an optimal control scheme, show the existence of an optimal control and a possible approximation strategy. We prove that the cost functional is lower semicontinuous with respect to the convergence of this approximation and argue that an optimal control is attained in the case that there exists a solution admitting additional regularity. 
M. Eigel, J. Neumann, R. Schneider, S. Wolf, Risk averse stochastic structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 334 (2018), pp. 470482, DOI 10.1016/j.cma.2018.02.003 .
Abstract
A novel approach for riskaverse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a highdimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common riskaware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such highdimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach. 
L. Adam, M. Hintermüller, Th.M. Surowiec, A PDEconstrained optimization approach for topology optimization of strained photonic devices, Annali di Matematica Pura ed Applicata. Serie Quarta. Fondazione Annali di Matematica Pura ed Applicata, c/o Dipartimento di Matematica ``U. Dini'', Firenze; SpringerVerlag, Heidelberg. English, French, German, Italian, English abstracts., 19 (2018), pp. 521557, DOI 10.1007/s1108101893945 .
Abstract
Recent studies have demonstrated the potential of using tensilestrained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multimaterial phasefield approach to determine the optimal material configuration within a socalled GermaniumonSilicon microbridge is considered. Here, an “optimal" configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the crosssection of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a nonlinear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and secondorder optimality conditions. For the numerical experiments, an array of first and secondorder solution algorithms in functionspace are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed. 
L. Adam, M. Hintermüller, Th.M. Surowiec, A semismooth Newton method with analytical pathfollowing for the $H^1$projection onto the Gibbs simplex, IMA Journal of Numerical Analysis, 39 (2019), pp. 12761295 (published online on 07.06.2018), DOI 10.1093/imanum/dry034 .
Abstract
An efficient, functionspacebased secondorder method for the $H^1$projection onto the Gibbssimplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as MoreauYosida regularization and techniques from parametric optimization. A pathfollowing technique is considered for the regularization parameter updates. A rigorous first and secondorder sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits meshindependent behavior. 
H. Antil, C.N. Rautenberg, Fractional elliptic quasivariational inequalities: Theory and numerics, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 20 (2018), pp. 124, DOI 10.4171/IFB/395 .

P. Colli, G. Gilardi, J. Sprekels, Optimal boundary control of a nonstandard viscous CahnHilliard system with dynamic boundary condition, Nonlinear Analysis. An International Mathematical Journal, 170 (2018), pp. 171196, DOI 10.1016/j.na.2018.01.003 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by PodioGuidugli in Ric. Mat. 55 (2006), pp. 105118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing control literature about this PDE system, we consider here a dynamic boundary condition involving the LaplaceBeltrami operator for the order parameter of the system, which models an additional nonconserving phase transition occurring on the surface of the domain. We show the Fr&aecute;chenett differentiability of the associated controltostate operator in appropriate Banach spaces and derive results on the existence of optimal controls and on firstorder necessary optimality conditions in terms of a variational inequality and the adjoint state system. 
P. Colli, G. Gilardi, J. Sprekels, Optimal distributed control of a generalized fractional CahnHilliard system, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 82 (2020), pp. 551589 (published online on 15.11.2018), DOI 10.1007/s0024501895407 .
Abstract
In the recent paper “Wellposedness and regularity for a generalized fractional CahnHilliard system” by the same authors, general wellposedness results have been established for a class of evolutionary systems of two equations having the structure of a viscous CahnHilliard system, in which nonlinearities of doublewell type occur. The operators appearing in the system equations are fractional versions in the spectral sense of general linear operators A,B, having compact resolvents, which are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. In this work we complement the results given in quoted paper by studying a distributed control problem for this evolutionary system. The main difficulty in the analysis is to establish a rigorous Fréchet differentiability result for the associated controltostate mapping. This seems only to be possible if the state stays bounded, which, in turn, makes it necessary to postulate an additional global boundedness assumption. One typical situation, in which this assumption is satisfied, arises when B is the negative Laplacian with zero Dirichlet boundary conditions and the nonlinearity is smooth with polynomial growth of at most order four. Also a case with logarithmic nonlinearity can be handled. Under the global boundedness assumption, we establish existence and firstorder necessary optimality conditions for the optimal control problem in terms of a variational inequality and the associated adjoint state system. 
P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a viscous CahnHilliard system with convection and dynamic boundary conditions, SIAM Journal on Control and Optimization, 56 (2018), pp. 16651691, DOI 10.1137/17M1146786 .
Abstract
In this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents an additional difficulty for the analysis. The nonlinearities in the bulk and surface free energies are of logarithmic type, which entails that the thermodynamic forces driving the phase separation process may become singular. We show existence for the optimal control problem under investigation, prove the Fréchet differentiability of the associated controltostate mapping in suitable Banach spaces, and derive the firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint system. Due to the strong nonlinear couplings between state variables and control, the corresponding proofs require a considerable analytical effort. 
S. Frigeri, M. Grasselli, J. Sprekels, Optimal distributed control of twodimensional nonlocal CahnHilliardNavierStokes systems with degenerate mobility and singular potential, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 81 (2020), pp. 889931 (published online on 24.09.2018), DOI 10.1007/s0024501895247 .
Abstract
In this paper, we consider a twodimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the NavierStokes equations, nonlinearly coupled with a convective nonlocal CahnHilliard equation. The system rules the evolution of the volumeaveraged velocity of the mixture and the (relative) concentration difference of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a timedependent external force acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the controltostate map, and we establish firstorder necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in [19]. There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in [14]. 
A. Hantoute, R. Henrion, P. PérezAros, Subdifferential characterization of probability functions under Gaussian distribution, Mathematical Programming. A Publication of the Mathematical Programming Society, 174 (2019), pp. 167194 (published online on 29.01.2018), DOI 10.1007/s1010701812379 .
Abstract
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates the consideration of subdifferentials for such typically just continuous functions. The aim of this paper is to provide subdifferential formulae of such functions in the case of Gaussian distributions for possibly infinitedimensional decision variables and nonsmooth (locally Lipschitzian) input data. These formulae are based on the sphericradial decomposition of Gaussian random vectors on the one hand and on a cone of directions of moderate growth on the other. By successively adding additional hypotheses, conditions are satisfied under which the probability function is locally Lipschitzian or even differentiable. 
R. Henrion, W. Römisch, Problembased optimal scenario generation and reduction in stochastic programming, Mathematical Programming. A Publication of the Mathematical Programming Society, pp. published online on 04.10.2018, urlhttps://doi.org/10.1007/s1010701813376, DOI 10.1007/s1010701813376 .
Abstract
Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear twostage stochastic programs we show that the problembased approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semiinfinite program. We show that the latter is convex if either righthand sides or costs are random and can be transformed into a semiinfinite program in a number of cases. We also consider problembased optimal scenario reduction for twostage models and optimal scenario generation for chance constrained programs. Finally, we discuss problembased scenario generation for the classical newsvendor problem. 
M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, A goaloriented dualweighted adaptive finite element approach for the optimal control of a nonsmooth CahnHilliardNavierStokes system, Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences, 19 (2018), pp. 629662, DOI 10.1007/s1108101893936 .
Abstract
This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a timediscrete CahnHilliardNavierStokes system with variable densities. The free energy density associated to the CahnHilliard system incorporates the doubleobstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the NavierStokes equation. A dualweighed residual approach for goaloriented adaptive finite elements is presented which is based on the concept of Cstationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given. 
M. Hintermüller, C.N. Rautenberg, N. Strogies, Dissipative and nondissipative evolutionary quasivariational inequalities with gradient constraints, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 27 (2019), pp. 433468 (published online on 14.07.2018), DOI 10.1007/s1122801804890 .
Abstract
Evolutionary quasivariational inequality (QVI) problems of dissipative and nondissipative nature with pointwise constraints on the gradient are studied. A semidiscretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and nondecrease in time, are derived. The proposed numerical solver reduces to a finite number of gradientconstrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints. 
M. Eigel, R. Müller, A posteriori error control for stationary coupled bulksurface equations, IMA Journal of Numerical Analysis, 38 (2018), pp. 271298 (published online on 09.03.2017), DOI 10.1093/imanum/drw080 .
Abstract
We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm with several benchmark examples. 
M. Eigel, K. Sturm, Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation, Optimization Methods & Software, 33 (2018), pp. 268296 (published online on 03.05.2017), DOI 10.1080/10556788.2017.1314471 .
Abstract
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments. 
L. Adam, R. Henrion, J. Outrata, On Mstationarity conditions in MPECs and the associated qualification conditions, Mathematical Programming. A Publication of the Mathematical Programming Society, 168 (2018), pp. 229259 (published online on 18.4.2017), DOI 10.1007/s1010701711463 .
Abstract
Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed constraint qualifications (CQs) as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible CQs, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive socalled Mstationarity conditions. The strength of assumptions and conclusions in the two forms of the MPEC is strongly related with the CQs on the 'lower level' imposed on the set whose normal cone appears in the generalized equation. For instance, under just the MangasarianFromovitz CQ (a minimum assumption required for this set), the calmness properties of the original and the enhanced perturbation mapping are drastically different. They become identical in the case of a polyhedral set or when adding the Full Rank CQ. On the other hand, the resulting optimality conditions are affected too. If the considered set even satisfies the Linear Independence CQ, both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. A compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions is provided in the main Theorem 4.3. The obtained results are finally applied to MPECs with structured equilibria. 
H. Antil, M. Hintermüller, R.H. Nochetto, Th.M. Surowiec, D. Wegner, Finite horizon model predictive control of electrowetting on dielectric with pinning, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 19 (2017), pp. 130, DOI 10.4171/IFB/375 .

H. Egger, Th. Kugler, N. Strogies, Parameter identification in a semilinear hyperbolic system, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 33 (2017), pp. 055022/1055022/25, DOI 10.1088/13616420/aa648c .
Abstract
We consider the identification of a nonlinear friction law in a onedimensional damped wave equation from additional boundary measurements. Wellposedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigate the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be illposed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings. 
M.H. Farshbaf Shaker, R. Henrion, D. Hömberg, Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 26 (2018), pp. 821841 (published online on 11.10.2017), DOI 10.1007/s1122801704525 .
Abstract
Chance constraints represent a popular tool for finding decisions that enforce a robust satisfaction of random inequality systems in terms of probability. They are widely used in optimization problems subject to uncertain parameters as they arise in many engineering applications. Most structural results of chance constraints (e.g., closedness, convexity, Lipschitz continuity, differentiability etc.) have been formulated in a finitedimensional setting. The aim of this paper is to generalize some of these wellknown semicontinuity and convexity properties to a setting of control problems subject to (uniform) state chance constraints. 
V. Guigues, R. Henrion, Joint dynamic probabilistic constraints with projected linear decision rules, Optimization Methods & Software, 32 (2017), pp. 10061032.
Abstract
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of waitandsee type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically. 
S. Hajian, M. Hintermüller, S. Ulbrich, Total variation diminishing schemes in optimal control of scalar conservation laws, IMA Journal of Numerical Analysis, 39 (2019), pp. 105140 (published online on 14.12.2017), DOI 10.1093/imanum/drx073 .
Abstract
In this paper, optimal control problems subject to a nonlinear scalar conservation law are studied. Such optimal control problems are challenging both at the continuous and at the discrete level since the controltostate operator poses difficulties as it is, e.g., not differentiable. Therefore discretization of the underlying optimal control problem should be designed with care. Here the discretizethenoptimize approach is employed where first the full discretization of the objective function as well as the underlying PDE is considered. Then, the derivative of the reduced objective is obtained by using an adjoint calculus. In this paper total variation diminishing RungeKutta (TVDRK) methods for the time discretization of such problems are studied. TVDRK methods, also called strong stability preserving (SSP), are originally designed to preserve total variation of the discrete solution. It is proven in this paper that providing an SSP state scheme, is enough to ensure stability of the discrete adjoint. However requiring SSP for both discrete state and adjoint is too strong. Also approximation properties that the discrete adjoint inherits from the discretization of the state equation are studied. Moreover order conditions are derived. In addition, optimal choices with respect to CFL constant are discussed and numerical experiments are presented. 
H. Meinlschmidt, Ch. Meyer, J. Rehberg, Optimal control of the thermistor problem in three spatial dimensions. Part 1: Existence of optimal solutions, SIAM Journal on Control and Optimization, 55 (2017), pp. 28762904, DOI 10.1137/16M1072644 .
Abstract
This paper is concerned with the stateconstrained optimal control of the threedimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive firstorder necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results. 
H. Meinlschmidt, Ch. Meyer, J. Rehberg, Optimal control of the thermistor problem in three spatial dimensions. Part 2: Optimality conditions, SIAM Journal on Control and Optimization, 55 (2017), pp. 23682392, DOI 10.1137/16M1072656 .
Abstract
This paper is concerned with the stateconstrained optimal control of the threedimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive firstorder necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results. 
W. VAN Ackooij, R. Henrion, (Sub) Gradient formulae for probability functions of random inequality systems under Gaussian distribution, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), pp. 6387, DOI 10.1137/16M1061308 .
Abstract
We consider probability functions of parameterdependent random inequality systems under Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential of such probability functions without imposing compactness conditions. A constraint qualification ensuring continuous differentiability is formulated. Explicit formulae are derived from the general result in case of linear random inequality systems. In the case of a constant coefficient matrix an upper estimate for even the smaller Mordukhovich subdifferential is proven. 
M. Hintermüller, T. Keil, D. Wegner, Optimal control of a semidiscrete CahnHilliardNavierStokes system with nonmatched fluid densities, SIAM Journal on Control and Optimization, 55 (2017), pp. 19541989.

M. Hintermüller, C.N. Rautenberg, M. Mohammadi, M. Kanitsar, Optimal sensor placement: A robust approach, SIAM Journal on Control and Optimization, 55 (2017), pp. 36093639.
Abstract
We address the problem of optimally placing sensor networks for convectiondiffusion processes where the convective part is perturbed. The problem is formulated as an optimal control problem where the integral Riccati equation is a constraint and the design variables are sensor locations. The objective functional involves a term associated to the trace of the solution to the Riccati equation and a term given by a constrained optimization problem for the directional derivative of the previous quantity over a set of admissible perturbations. The paper addresses the existence of the derivative with respect to the convective part of the solution to the Riccati equation, the wellposedness of the optimization problem and finalizes with a range of numerical tests. 
M. Hintermüller, C.N. Rautenberg, S. Rösel, Density of convex intersections and applications, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 473 (2017), pp. 20160919/120160919/28, DOI 10.1098/rspa.2016.0919 .
Abstract
In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gammaconvergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elastoplasticity and image restoration problems. 
M. Eigel, Ch. Merdon, Equilibration a posteriori error estimation for convectiondiffusionreaction problems, Journal of Scientific Computing, 67 (2016), pp. 747768.
Abstract
We study a posteriori error estimates for convectiondiffusionreaction problems with possibly dominating convection or reaction and inhomogeneous boundary conditions. For the conforming FEM discretisation with streamline diffusion stabilisation (SDM), we derive robust and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of H (div, Ω). Error estimators of this type have become popular recently since they provide guaranteed error bounds without further unknown constants. The estimators can be improved significantly by some postprocessing and divergence correction technique. For an extension of the energy norm by a dual norm of some part of the differential operator, complete independence from the coefficients of the problem is achieved.Numerical benchmarks illustrate the very good performance of the error estimators in the convection dominated and the singularly perturbed cases.

D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410423.
Abstract
We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantumwell lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights. 
M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Outer limit of subdifferentials and calmness moduli in linear and nonlinear programming, Journal of Optimization Theory and Applications, 169 (2016), pp. 925952.
Abstract
With a common background and motivation, the main contributions of this paper are developed in two different directions. Firstly, we are concerned with functions which are the maximum of a finite amount of continuously differentiable functions of n real variables, paying attention to the case of polyhedral functions. For these maxfunctions, we obtain some results about outer limits of subdifferentials, which are applied to derive an upper bound for the calmness modulus of nonlinear systems. When confined to the convex case, in addition, a lower bound on this modulus is also obtained. Secondly, by means of a KKT index set approach, we are also able to provide a pointbased formula for the calmness modulus of the argmin mapping of linear programming problems without any uniqueness assumption on the optimal set. This formula still provides a lower bound in linear semiinfinite programming. Illustrative examples are given. 
M.J. Cánovas, R. Henrion, J. Parra, F.J. Toledo, Critical objective size and calmness modulus in linear programming, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 24 (2016), pp. 565579.
Abstract
This paper introduces the concept of critical objective size associated with a linear program in order to provide operative pointbased formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in citeCHPTmp. In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to explore some strategies that can improve the referred upper and lower bounds. 
C. Carstensen, M. Eigel, Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on redrefined meshes, Computational Methods in Applied Mathematics, 16 (2016), pp. 213230.
Abstract
A hierarchical a posteriori error estimator for the firstorder finite element method (FEM) on a redrefined triangular mesh is presented for the 2D Poisson model problem. Reliability and efficiency with some explicit constant is proved for triangulations with inner angles smaller than or equal to pi/2. The error estimator does not rely on any saturation assumption and is valid even in the preasymptotic regime on arbitrarily coarse meshes. The evaluation of the estimator is a simple postprocessing of the piecewise linear FEM without any extra solve plus a higherorder approximation term. The results also allows the striking observation that arbitrary local averaging of the primal variable leads to a reliable and efficient error estimation. Several numerical experiments illustrate the performance of the proposed a posteriori error estimator for computational benchmarks. 
P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the viscous CahnHilliard equation with dynamic boundary conditions, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 73 (2016), pp. 195225, DOI 10.1007/s002450159299z .
Abstract
A boundary control problem for the viscous CahnHilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. 
P. Colli, G. Gilardi, J. Sprekels, Constrained evolution for a quasilinear parabolic equation, Journal of Optimization Theory and Applications, 170 (2016), pp. 713734.
Abstract
In the present contribution, a feedback control law is studied for a quasilinear parabolic equation. First, we prove the wellposedness and some regularity results for the CauchyNeumann problem for this equation, modified by adding an extra term which is a multiple of the subdifferential of the distance function from a closed convex set K of L^{2}(Ω). Then, we consider convex sets of obstacle or doubleobstacle type, and we can act on the factor of the feedback control in order to be able to reach the convex set within a finite time, by proving rigorously this property. 
P. Colli, G. Gilardi, J. Sprekels, Distributed optimal control of a nonstandard nonlocal phase field system, AIMS Mathematics, 1 (2016), pp. 246281.
Abstract
We investigate a distributed optimal control problem for a nonlocal phase field model of viscous CahnHilliard type. The model constitutes a nonlocal version of a model for twospecies phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. PodioGuidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the firstorder necessary conditions of optimality. 
G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, Journal of Differential Equations, 260 (2016), pp. 33973447.
Abstract
The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolzatype functional, which depends on control and state variables as well as their velocities. Besides the highly nonLipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of firstorder and secondorder variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a byproduct of the developed approach, we prove the strong W^{1,2}convergence of optimal solutions of discrete approximations to a given local minimizer of the continuoustime system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples. 
A. Gasnikov, P. Dvurechensky, Y. Dorn, Y. Maximov, Numerical methods for finding equilibrium flow distribution in Beckman and stable dynamics models, Rossiiskaya Akademiya Nauk. Matematicheskoe Modelirovanie, 28 (2016), pp. 4064.

H. Meinlschmidt, J. Rehberg, Hölderestimates for nonautonomous parabolic problems with rough data, Evolution Equations and Control Theory, 5 (2016), pp. 147184.
Abstract
In this paper we establish Hölder estimates for solutions to nonautonomous parabolic equations on nonsmooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al., which also serves as the starting point for our investigations. 
K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016), pp. 557588.
Abstract
We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface. 
M.H. Farshbaf Shaker, C. Hecht, Optimal control of elastic vectorvalued AllenCahn variational inequalities, SIAM Journal on Control and Optimization, 54 (2016), pp. 129152.
Abstract
In this paper we consider a elastic vectorvalued AllenCahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized firstorder necessary optimality conditions for the original problem. 
S.P. Frigeri, E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal CahnHilliard/NavierStokes system in two dimensions, SIAM Journal on Control and Optimization, 54 (2016), pp. 221  250.
Abstract
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the NavierStokes system with a convective nonlocal CahnHilliard equation in two dimensions of space. We apply recently proved wellposedness and regularity results in order to establish existence of optimal controls as well as firstorder necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow. 
CH. Heinemann, K. Sturm, Shape optimisation for a class of semilinear variational inequalities with applications to damage models, SIAM Journal on Mathematical Analysis, 48 (2016), pp. 35793617, DOI 10.1137/16M1057759 .
Abstract
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise from another optimisation problems. We prove a strong convergence property for the material derivative and establish stateshape derivatives under regularity assumptions. Finally, as a concrete application from continuum mechanics, we show how the dynamic obstacle case can be used to treat shape optimisation problems for timediscretised brittle damage models for elastic solids. We derive a necessary optimality system for optimal shapes whose state variables approximate desired damage patterns and/or displacement fields. 
M. Hintermüller, Th. Surowiec, A bundlefree implicit programming approach for a class of elliptic MPECs in function space, Mathematical Programming Series A, 160 (2016), pp. 271305.

E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal convective CahnHilliard equation by the velocity in three dimensions, SIAM Journal on Control and Optimization, 53 (2015), pp. 16541680.
Abstract
In this paper we study a distributed optimal control problem for a nonlocal convective CahnHilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system of PDEs containing singular and degenerating terms, and the control variable, which is given by the velocity of the motion occurring in the convective term, is nonlinearly coupled to the state variable. The latter fact makes it necessary to state rather special regularity assumptions for the admissible controls, which, while looking a bit nonstandard, are however quite natural in the corresponding analytical framework. In fact, they are indispensable prerequisites to guarantee the wellposedness of the associated state system. In this contribution, we employ recently proved existence, uniqueness and regularity results for the solution to the associated state system in order to establish the existence of optimal controls and appropriate firstorder necessary optimality conditions for the optimal control problem. 
P.É. Druet, Some mathematical problems related to the second order optimal shape of a crystallization interface, Discrete and Continuous Dynamical Systems, 35 (2015), pp. 24432463.
Abstract
We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solidliquid interface in a twophase system subject to a temperature gradient. The interface satisfies the minimization principle of the free energy, while the temperature is solving the heat equation with a radiation boundary conditions at the outer wall. Under the condition that the temperature gradient is uniformly negative in the direction of crystallization, the interface is expected to have a global graph representation. We reformulate this condition as a pointwise constraint on the gradient of the state, and we derive the first order optimality system for a class of objective functionals that account for the second surface derivatives, and for the surface temperature gradient. 
M. Eigel, D. Peterseim, Simulation of composite materials by a Network FEM with error control, Computational Methods in Applied Mathematics, 15 (2015), pp. 2137.
Abstract
A novel Finite Element Method (FEM) for the computational simulation in particle reinforced composite materials with many inclusions is presented. It is based on a specially designed mesh consisting of triangles and channellike connections between inclusions which form a network structure. The total number of elements and, hence, the number of degrees of freedom are proportional to the number of inclusions. The error of the method is independent of the possibly tiny distances of neighbouring inclusions.We present algorithmic details for the generation of the problem adapted mesh and derive an efficient residual a posteriori error estimator which enables to compute reliable upper and lower error bounds. Several numerical examples illustrate the performance of the method and the error estimator. In particular, it is demonstrated that the (common) assumption of a lattice structure of inclusions can easily lead to incorrect predictions about material properties.

P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the pure CahnHilliard equation with dynamic boundary conditions, Advances in Nonlinear Analysis, 4 (2015), pp. 311325.
Abstract
A boundary control problem for the pure CahnHilliard equations with possibly singular potentials and dynamic boundary conditions is studied and firstorder necessary conditions for optimality are proved. 
P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Optimal boundary control of a viscous CahnHilliard system with dynamic boundary condition and double obstacle potentials, SIAM Journal on Control and Optimization, 53 (2015), pp. 26962721.
Abstract
In this paper, we investigate optimal boundary control problems for CahnHilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the LaplaceBeltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive firstorder necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, FarshbafShaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) AllenCahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a socalled “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired firstorder necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials. 
P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Secondorder analysis of a boundary control problem for the viscous CahnHilliard equation with dynamic boundary conditions, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 7 (2015), pp. 4166.
Abstract
In this paper we establish secondorder sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous CahnHilliard equation with possibly singular potentials and dynamic boundary conditions. 
P. Colli, M.H. Farshbaf Shaker, J. Sprekels, A deep quench approach to the optimal control of an AllenCahn equation with dynamic boundary conditions and double obstacles, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 71 (2015), pp. 124.
Abstract
In this paper, we investigate optimal control problems for AllenCahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the LaplaceBeltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive firstorder necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors for the case of (differentiable) logarithmic potentials and perform a socalled “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired firstorder necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials. 
P. Colli, J. Sprekels, Optimal control of an AllenCahn equation with singular potentials and dynamic boundary condition, SIAM Journal on Control and Optimization, 53 (2015), pp. 213234.
Abstract
In this paper, we investigate optimal control problems for AllenCahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the LaplaceBeltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. Parabolic problems with nonlinear dynamic boundary conditions involving the LaplaceBeltrami operation have recently drawn increasing attention due to their importance in applications, while their optimal control was apparently never studied before. In this paper, we first extend known wellposedness and regularity results for the state equation and then show the existence of optimal controls and that the controltostate mapping is twice continuously Fréchet differentiable between appropriate function spaces. Based on these results, we establish the firstorder necessary optimality conditions in terms of a variational inequality and the adjoint state equation, and we prove secondorder sufficient optimality conditions. 
G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Discrete approximations of a controlled sweeping process, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 23 (2015), pp. 6986.

W. Giese, M. Eigel, S. Westerheide, Ch. Engwer, E. Klipp, Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models, Physical Biology, 12 (2015), pp. 066014/1066014/18.
Abstract
In silico experiments bear the potential to further the understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results for the chosen models. We consider cell polarization and spatial reorganization of membrane proteins which are fundamental for cell division, chemotaxis and morphogenesis. Our computational study is motivated by mating and budding processes of S. cerevisiae. In these processes a key player during the initial phase of polarization is the GTPase Cdc42 which occurs in an active membranebound form and an inactive cytosolic form. We use partial differential equations to describe the membranecytosol shuttling of Cdc42 during budding as well as mating of yeast. The membrane is modeled as a thin layer that only allows lateral diffusion and the cytosol is modeled as a volume. We investigate how cell shape and diffusion barriers like septin structures or bud scars influence Cdc42 cluster formation and subsequent polarization of the yeast cell. Since the details of the binding kinetics of cytosolic proteins to the membrane are still controversial, we employ two conceptual models which assume different binding kinetics. An extensive set of in silico experiments with different modeling hypotheses illustrate the qualitative dependence of cell polarization on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. We examine that spatial inhomogenities essentially determine the location of Cdc42 cluster formation and spatial properties are crucial for the realistic description of the polarization process in cells. In particular, our computer simulations suggest that diffusion barriers are essential for the yeast cell to grow a protrusion. 
P. Dvurechensky, Y. Nesterov, V. Spokoiny, Primaldual methods for solving infinitedimensional games, Journal of Optimization Theory and Applications, 166 (2015), pp. 2351.

M.H. Farshbaf Shaker, A relaxation approach to vectorvalued AllenCahn MPEC problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 72 (2015), pp. 325351.

M.H. Farshbaf Shaker, Ch. Heinemann, A phase field approach for optimal boundary control of damage processes in twodimensional viscoelastic media, Mathematical Models & Methods in Applied Sciences, 25 (2015), pp. 27492793.
Abstract
In this work we investigate a phase field model for damage processes in twodimensional viscoelastic media with nonhomogeneous Neumann data describing external boundary forces. In the first part we establish globalintime existence, uniqueness, a priori estimates and continuous dependence of strong solutions on the data. The main difficulty is caused by the irreversibility as well as boundedness of the phase field variable which results in a doubly constrained PDE system. In the last part we consider an optimal control problem where a cost functional penalizes maximal deviations from prescribed damage profiles. The goal is to minimize the cost functional with respect to exterior forces acting on the boundary which play the role of the control variable in the considered model . To this end, we prove existence of minimizers and study a family of “local” approximations via adapted cost functionals. 
TH. Arnold, R. Henrion, A. Möller, S. Vigerske, A mixedinteger stochastic nonlinear optimization problem with joint probabilistic constraints, Pacific Journal of Optimization. An International Journal, 10 (2014), pp. 520.
Abstract
We illustrate the solution of a mixedinteger stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated. 
M. Eigel, T. Samrowski, Functional a posteriori error estimation for stationary reactionconvectiondiffusion problems, Computational Methods in Applied Mathematics, 14 (2014), pp. 135150.
Abstract
A functional type a posteriori error estimator for the finite element discretisation of the stationary reactionconvectiondiffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shockfront like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no meshdependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimisation problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator and compare it with some classic a posteriori error estimators often used in practice. It is observed that the new estimator exhibits a good efficiency also with convectiondominated problem settings. 
K. Emich, R. Henrion, W. Römisch, Conditioning of linearquadratic twostage stochastic optimization problems, Mathematical Programming. A Publication of the Mathematical Programming Society, 148 (2014), pp. 201221.
Abstract
In this paper a condition number for linearquadratic twostage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number can be estimated from above explicitly in terms of the problem data by applying appropriate calculus rules. Here, a chain rule for the extended partial secondorder subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role. The obtained results are illustrated for the example of twostage stochastic optimization problems with simple recourse. 
K. Emich, R. Henrion, A simple formula for the secondorder subdifferential of maximum functions, Vietnam Journal of Mathematics, 42 (2014), pp. 467478.
Abstract
We derive a simple formula for the secondorder subdifferential of the maximum of coordinates which allows us to construct this set immediately from its argument and the direction to which it is applied. This formula can be combined with a chain rule recently proved by Mordukhovich and Rockafellar [9] in order to derive a similarly simple formula for the extended partial secondorder subdifferential of finite maxima of smooth functions. Analogous formulae can be derived immediately for the full and conventional partial secondorder subdifferentials. 
R. Hildebrand, Hessian potentials with parallel derivatives, Results in Mathematics, 65 (2014), pp. 399413.

R. Hildebrand, Minimal zeros of copositive matrices, Linear Algebra and its Applications, 459 (2014), pp. 154174.
Abstract
Let A be an element of the copositive cone CnCn. A zero u of A is a nonzero nonnegative vector such that uTAu=0uTAu=0. The support of u is the index set View the MathML sourcesuppu?1,?,n corresponding to the positive entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u . We investigate the properties of minimal zeros of copositive matrices and their supports. Special attention is devoted to copositive matrices which are irreducible with respect to the cone S+(n)S+(n) of positive semidefinite matrices, i.e., matrices which cannot be written as a sum of a copositive and a nonzero positive semidefinite matrix. We give a necessary and sufficient condition for irreducibility of a matrix A with respect to S+(n)S+(n) in terms of its minimal zeros. A similar condition is given for the irreducibility with respect to the cone NnNn of entrywise nonnegative matrices. For n=5n=5 matrices which are irreducible with respect to both S+(5)S+(5) and N5N5 are extremal. For n=6n=6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided. 
L. Blank, M.H. Farshbaf Shaker, H. Garcke, V. Styles, Relating phase field and sharp interface approaches to structural topology optimization, ESAIM. Control, Optimisation and Calculus of Variations, 20 (2014), pp. 10251058.
Abstract
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. 
W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014), pp. 13281333.
Abstract
In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg. 
A. Fügenschuh, B. Geissler, Ch. Hayn, R. Henrion, B. Hiller, J. Humpola, Th. Koch ET AL., Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets, Energy Systems, 5 (2014), pp. 449473.

W. VAN Ackooij, R. Henrion, Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussianlike distributions, SIAM Journal on Optimization, 24 (2014), pp. 18641889.
Abstract
Probabilistic constraints represent a major model of stochastic optimization. A possible approach for solving probabilistically constrained optimization problems consists in applying nonlinear programming methods. In order to do so, one has to provide sufficiently precise approximations for values and gradients of probability functions. For linear probabilistic constraints under Gaussian distribution this can be successfully done by analytically reducing these values and gradients to values of Gaussian distribution functions and computing the latter, for instance, by Genz' code. For nonlinear models one may fall back on the sphericalradial decomposition of Gaussian random vectors and apply, for instance, Deák's sampling scheme for the uniform distribution on the sphere in order to compute values of corresponding probability functions. The present paper demonstrates how the same sampling scheme can be used in order to simultaneously compute gradients of these probability functions. More precisely, we prove a formula representing these gradients in the Gaussian case as a certain integral over the sphere again. Later, the result is extended to alternative distributions with an emphasis on the multivariate Student (or T) distribution. 
D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in nonisothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014), pp. 035003/1035003/24.
Abstract
We study nonisothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation. 
P. Colli, G. Gilardi, P. PodioGuidugli, J. Sprekels, An asymptotic analysis for a nonstandard CahnHilliard system with viscosity, Discrete and Continuous Dynamical Systems  Series S, 6 (2013), pp. 353368.
Abstract
This paper is concerned with a diffusion model of phasefield type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order parameter $rho$ and the chemical potential $mu$; each equation includes a viscosity term  respectively, $varepsilon,partial_tmu$ and $delta,partial_trho$  with $varepsilon$ and $delta$ two positive parameters; the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In a recent paper [5], we proved that this problem is wellposed and investigated the longtime behavior of its $(varepsilon,delta)$solutions. Here we discuss the asymptotic limit of the system as $eps$ tends to 0. We prove convergence of $(varepsilon,delta)$solutions to the corresponding solutions for the case $eps$ =0, whose longtime behavior we characterize; in the proofs, we employ compactness and monotonicity arguments. 
K. Krumbiegel, J. Rehberg, Second order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints, SIAM Journal on Control and Optimization, 51 (2013), pp. 301331.
Abstract
In this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations. 
R. Henrion, A. Kruger, J. Outrata, Some remarks on stability of generalized equations, Journal of Optimization Theory and Applications, 159 (2013), pp. 681697.
Abstract
The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by $C^2$ inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, one assumes a combination of the MangasarianFromovitz and the Constant Rank qualification conditions. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided. 
D. Hömberg, K. Krumbiegel, J. Rehberg, Optimal control of a parabolic equation with dynamic boundary condition, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 67 (2013), pp. 331.
Abstract
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the Robin boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an $L^p$ function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions. 
P. Colli, G. Gilardi, P. PodioGuidugli, J. Sprekels, Distributed optimal control of a nonstandard system of phase field equations, Continuum Mechanics and Thermodynamics, 24 (2012), pp. 437459.
Abstract
We investigate a distributed optimal control problem for a phase field model of CahnHilliard type. The model describes twospecies phase segregation on an atomic lattice under the presence of diffusion; it has been introduced recently in [4], on the basis of the theory developed in [15], and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the firstorder necessary conditions of optimality. 
P. Colli, G. Gilardi, J. Sprekels, Analysis and optimal boundary control of a nonstandard system of phase field equations, Milan Journal of Mathematics, 80 (2012), pp. 119149.
Abstract
We investigate a nonstandard phase field model of CahnHilliard type. The model, which was introduced in PodioGuidugli (2006), describes twospecies phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in Colli, Gilardi, PodioGuidugli, and Sprekels (2011a and b) for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show wellposedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the firstorder necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type. 
G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process, Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, 19 (2012), pp. 117159.

M. Gerdts, R. Henrion, D. Hömberg, Ch. Landry, Path planning and collision avoidance for robots, Numerical Algebra, Control and Optimization, 2 (2012), pp. 437463.
Abstract
An optimal control problem to find the fastest collisionfree trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique. 
R. Henrion, J. Outrata, Th. Surowiec, Analysis of Mstationary points to an EPEC modeling oligopolistic competition in an electricity spot market, ESAIM. Control, Optimisation and Calculus of Variations, 18 (2012), pp. 295317.
Abstract
We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, socalled $M$stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify $M$stationarity. Third, for stating the stationarity conditions, the coderivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple twosettlements example serves as an illustration. 
W. Dreyer, P.É. Druet, O. Klein, J. Sprekels, Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals, Milan Journal of Mathematics, 80 (2012), pp. 311332.
Abstract
This paper deals with the mathematical modeling and simulation of crystal growth processes by the socalled Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initialboundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of reallife growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years. 
R. Henrion, J. Outrata, Th. Surowiec, On regular coderivatives in parametric equilibria with nonunique multiplier, Mathematical Programming. A Publication of the Mathematical Programming Society, 136 (2012), pp. 111131.

K. Krumbiegel, I. Neitzel, A. Rösch, Regularization error estimates for semilinear elliptic optimal control problems with pointwise state and control constraints, Computational Optimization and Applications. An International Journal, 52 (2012), pp. 181207.
Abstract
In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. A sufficient second order optimality condition and uniqueness of the dual variables are assumed for that problem. Sufficient second order optimality conditions are shown for regularized problems with small regularization parameter. Moreover, error estimates with respect to the regularization parameter are derived. 
P.É. Druet, O. Klein, J. Sprekels, F. Tröltzsch, I. Yousept, Optimal control of threedimensional stateconstrained induction heating problems with nonlocal radiation effects, SIAM Journal on Control and Optimization, 49 (2011), pp. 17071736.
Abstract
The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, timeharmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperaturedependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the controltostate mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established. 
R. Henrion, Th. Surowiec, On calmness conditions in convex bilevel programming, Applicable Analysis. An International Journal, 90 (2011), pp. 951970.
Abstract
In this article we compare two different calmness conditions which are widely used in the literature on bilevel programming and on mathematical programs with equilibrium constraints. In order to do so, we consider convex bilevel programming as a kind of intersection between both research areas. The socalled partial calmness concept is based on the function value approach for describing the lower level solution set. Alternatively, calmness in the sense of multifunctions may be considered for perturbations of the generalized equation representing the same lower level solution set. Both concepts allow to derive first order necessary optimality conditions via tools of generalized differentiation introduced by Mordukhovich. They are very different, however, concerning their range of applicability and the form of optimality conditions obtained. The results of this paper seem to suggest that partial calmness is considerably more restrictive than calmness of the perturbed generalized equation. This fact is also illustrated by means of a dicretized obstacle control problem. 
R. Henrion, C. Strugarek, Convexity of chance constraints with dependent random variables: The use of copulae, International Series in Operations Research & Management Science, 163 (2011), pp. 427439.

J. Sprekels, D. Tiba, Extensions of the control variational method, Control and Cybernetics, 40 (2011), pp. 10991108.
Abstract
The control variational method is a development of the variational approach, based on optimal control theory. In this work, we give an application to a variational inequality arising in mechanics and involving unilateral conditions both in the domain and on the boundary, and we explore the extension of the method to timedependent problems. 
A. Caboussat, Ch. Landry, J. Rappaz, Optimization problem coupled with differential equations: A numerical algorithm mixing an interiorpoint method and event detection, Journal of Optimization Theory and Applications, 147 (2010), pp. 141156.

M.J. Fabian, R. Henrion, A.Y. Kruger, J. Outrata, Error bounds: Necessary and sufficient conditions, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 121149.
Abstract
The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivativelike objects both from the primal as well as from the dual space are used to characterize the error bound property of extendedrealvalued functions on a Banach space. 
R. Henrion, B. Mordukhovich, N.M. Nam, Secondorder analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM Journal on Optimization, 20 (2010), pp. 21992227.

R. Henrion, J. Outrata, Th. Surowiec, A note on the relation between strong and Mstationarity for a class of mathematical programs with equilibrium constraints, Kybernetika. The Journal of the Czech Society for Cybernetics and Information Sciences. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague. English., 46 (2010), pp. 423434.
Abstract
In this paper, we consider the characterization of strong stationary solutions to equilibrium problems with equilibrium constraints (EPECs). Assuming that the underlying generalized equation satisfies strong regularity in the sense of Robinson, an explicit multiplierbased stationarity condition can be derived. This is applied then to an equilibrium model arising from ISOregulated electricity spot markets. 
R. Henrion, W. Römisch, Lipschitz and differentiability properties of quasiconcave and singular normal distribution functions, Annals of Operations Research, 177 (2010), pp. 115125.

R. Henrion, A. Seeger, Inradius and circumradius of various convex cones arising in applications, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 483511.

D. Hömberg, Ch. Meyer, J. Rehberg, W. Ring, Optimal control for the thermistor problem, SIAM Journal on Control and Optimization, 48 (2010), pp. 34493481.
Abstract
This paper is concerned with the stateconstrained optimal control of the twodimensional thermistor problem, a quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive firstorder necessary conditions for the optimal control problem. 
K. Krumbiegel, Ch. Meyer, A. Rösch, A priori error analysis for linear quadratic elliptic Neumann boundary control problems with control and state constraints, SIAM Journal on Control and Optimization, 48 (2010), pp. 51085142.

K. Krumbiegel, I. Neitzel, A. Rösch, Sufficient optimality conditions for the MoreauYosidatype regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 2 (2010), pp. 222246.
Abstract
We develop sufficient optimality conditions for a MoreauYosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of MoreauYosida regularization to a special setting of the virtual control concept, for which standard second order sufficient conditions have been shown. Moreover, we compare both regularization approaches within a numerical example. 
R. Henrion, A. Seeger, On properties of different notions of centers for convex cones, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 205231.

R. Henrion, Ch. Küchler, W. Römisch, Scenario reduction in stochastic programming with respect to discrepancy distances, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 6793.

R. Henrion, J. Outrata, Th. Surowiec, On the coderivative of normal cone mappings to inequality systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 71 (2009), pp. 12131226.
Abstract
The paper deals with coderivative formulae for normal cone mappings to smooth inequality systems. Both, the regular (Linear Independence Constraint Qualification satisfied) and nonregular (MangasarianFromovitz Constraint Qualification satisfied) case are considered. A major part of the results relies on general transformation formulae previously obtained by Mordukhovich and Outrata. This allows to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by Mordukhovich and Outrata applies, however a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. A series of examples illustrates the use and comparison of the presented formulae. 
D. Hömberg, D. Kern, The heat treatment of steel  A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009), pp. 438442.
Abstract
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machinebased control. 
D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009), pp. 669681.
Abstract
The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solidsolid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results. 
K. Krumbiegel, A. Rösch, A virtual control concept for state constrained optimal control problems, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 213233.

J. Sprekels, D. Tiba, The control variational approach for differential systems, SIAM Journal on Control and Optimization, 47 (2009), pp. 32203236.

P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008), pp. 793799.
Abstract
The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations. 
R. Henrion, Ch. Küchler, W. Römisch, Discrepancy distances and scenario reduction in twostage stochastic integer programming, Journal of Industrial and Management Optimization, 4 (2008), pp. 363384.

R. Henrion, J. Outrata, On calculating the normal cone to a finite union of convex polyhedra, Optimization. A Journal of Mathematical Programming and Operations Research, 57 (2008), pp. 5778.

R. Henrion, A. Seeger, Uniform boundedness of norms of convex and nonconvex processes, Numerical Functional Analysis and Optimization. An International Journal, 29 (2008), pp. 551573.

R. Henrion, C. Strugarek, Convexity of chance constraints with independent random variables, Computational Optimization and Applications. An International Journal, 41 (2008), pp. 263276.

D. Dentcheva, R. Henrion, A. Ruszczynski, Stability and sensitivity of optimization problems with first order stochastic dominance constraints, SIAM Journal on Optimization, 18 (2007), pp. 322337.

C. Lefter, J. Sprekels, Optimal boundary control of a phase field system modeling nonisothermal phase transitions, Advances in Mathematical Sciences and Applications, 17 (2007), pp. 181194.

R. Henrion, W. Römisch, On Mstationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling, Applications of Mathematics, 522 (2007), pp. 473494.
Abstract
Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multileaderfollower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata [17]. For applying the general result an explicit representation of the coderivative of the normal cone mapping to a polyhedron is derived (Proposition 3.2). Later the coderivative formula is used for verifying constraint qualifications and for identifying Mstationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios. 
R. Henrion, Structural properties of linear probabilistic constraints, Optimization. A Journal of Mathematical Programming and Operations Research, 56 (2007), pp. 425440.

R. Henrion, A. Lewis, A. Seeger, Distance to uncontrollability for convex processes, SIAM Journal on Optimization, 45 (2006), pp. 2650.

R. Henrion, Some remarks on valueatrisk optimization, International Journal of Management Science and Engineering Management, 1 (2006), pp. 111118.

V. Arnăutu, J. Sprekels, D. Tiba, Optimization problems for curved mechanical structures, SIAM Journal on Control and Optimization, 44 (2005), pp. 743775.

R. Henrion, J. Outrata, Calmness of constraint systems with applications, Mathematical Programming. A Publication of the Mathematical Programming Society, 104 (2005), pp. 437464.

P. Bosch, A. Jourani, R. Henrion, Sufficient conditions for error bounds and applications, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 50 (2004), pp. 161181.

R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Mathematical Programming. A Publication of the Mathematical Programming Society, 100 (2004), pp. 589611.

R. Henrion, A. Möller, Optimization of a continuous distillation process under random inflow rate, Computers & Mathematics with Applications. An International Journal, 45 (2003), pp. 247262.

D. Hömberg, J. Sokolowski, Optimal shape design of inductor coils for induction hardening, SIAM Journal on Control and Optimization, 42 (2003), pp. 10871117.

D. Hömberg, S. Volkwein, Control of laser surface hardening by a reducedorder approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003), pp. 10031028.

J. Sprekels, D. Tiba, Optimization of clamped plates with discontinuous thickness, Systems & Control Letters, 48 (2003), pp. 289295.

A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches, SIAM Journal on Control and Optimization, 40 (2001), pp. 11071133.

V. Arnăutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 337354.

J. Sprekels, D. Tiba, Sur les arches lipschitziennes, Comptes Rendus Mathematique. Academie des Sciences. Paris, 331 (2000), pp. 179184.
Beiträge zu Sammelwerken

P. Colli, G. Gilardi, J. Sprekels, Deep quench approximation and optimal control of general CahnHilliard systems with fractional operators and double obstacle potentials, in: Analysis of Evolutionary and Complex Systems: Issue on the Occasion of Alexander Mielke's 60th Birthday, M. Liero, S. Reichelt, G. Schneider, F. Theil, M. Thomas, eds., 14 of Discrete and Continuous Dynamical Systems  Series S, American Institute of Mathematical Sciences, Springfield, 2021, pp. 243271, DOI 10.3934/dcdss.2020213 .
Abstract
Recently, the authors derived wellposedness and regularity results for general evolutionary operator equations having the structure of a CahnHilliard system. The involved operators were fractional versions in the spectral sense of general linear operators that have compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions. The class of admissible doublewell potentials driving the phase separation process modeled by the CahnHilliard system included polynomial, logarithmic, and double obstacle nonlinearities. In a subsequent paper, distributed optimal control problems for such systems were investigated, where only differentiable polynomial and logarithmic potentials were admitted. Existence of optimizers and firstorder optimality conditions were derived. In this paper, these results are complemented for nondifferentiable double obstacle nonlinearities. It is well known that for such nonlinearities standard constraint qualifications to construct Lagrange multipliers cannot be applied. To overcome this difficulty, we follow the socalled “deep quench” method, which has proved to be a powerful tool in optimal control problems with double obstacle potentials. We give a general convergence analysis of the deep quench approximation, including an error estimate, and demonstrate that its use leads to meaningful firstorder necessary optimality conditions. 
A. Alphonse, M. Hintermüller, C.N. Rautenberg, Recent trends and views on elliptic quasivariational inequalities, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 131.

P. Colli, G. Gilardi, J. Sprekels, Nonlocal phase field models of viscous CahnHilliard type, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 71100, DOI 10.1007/9783030331160 .
Abstract
A nonlocal phase field model of viscous CahnHilliard type is considered. This model constitutes a nonlocal version of a model for twospecies phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. PodioGuidugli and the present authors. The resulting system of differential equations consists of a highly nonlinear parabolic equation coupled to a nonlocal ordinary differential equation, which has singular terms that render the analysis difficult. Some results are presented on the wellposedness and stability of the system as well as on the distributed optimal control problem. 
M. Hintermüller, N. Strogies, On the consistency of RungeKutta methods up to order three applied to the optimal control of scalar conservation laws, in: Numerical Analysis and Optimization, M. AlBaali, L. Grandinetti, A. Purnama, eds., 235 of Springer Proceedings in Mathematics & Statistics, Springer Nature Switzerland AG, Cham, 2019, pp. 119154.
Abstract
Higherorder RungeKutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RKcoefficients are derived that coincide with those characterizing strong stability preserving RungeKutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a thirdorder method. Finally, numerical tests for controlling Burgers equation validate the theoretical results. 
M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Indexation strategies and calmness constants for uncertain linear inequality systems, in: The Mathematics of the Uncertain, E. Gil, E. Gil, J. Gil, M.Á. Gil, eds., 142 of Studies in Systems, Decision and Control, Springer, 2018, pp. 831843.

P. Dvurechensky, A. Gasnikov, A. Kroshnin, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, in: Proceedings of the 35th International Conference on Machine Learning, J. Dy, A. Krause, eds., 80 of Proceedings of Machine Learning Research, 2018, pp. 13671376.

M. Hintermüller, T. Keil, Some recent developments in optimal control of multiphase flows, in: Shape Optimization, Homogenization and Optimal Control. DFGAIMS Workshop held at the AIMS Center Senegal, March 1316, 2017, V. Schulz, D. Seck, eds., 169 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2018, pp. 113142, DOI 10.1007/9783319904696_7 .

P. Colli, J. Sprekels, Optimal boundary control of a nonstandard CahnHilliard system with dynamic boundary condition and double obstacle inclusions, in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., 22 of Springer INdAM Series, Springer International Publishing AG, Cham, 2017, pp. 151182, DOI 10.1007/9783319644899 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P.PodioGuidugli in Ric. Mat. 55 (2006), pp.105118. The model consists of a strongly coupled system of nonlinear parabolic differential inclusions, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically; the system is complemented by initial and boundary conditions. For the order parameter of the phase separation process, a dynamic boundary condition involving the LaplaceBeltrami operator is assumed, which models an additional nonconserving phase transition occurring on the surface of the domain. We complement in this paper results that were established in the recent contribution appeared in Evol. Equ. Control Theory 6 (2017), pp. 3558, by the two authors and Gianni Gilardi. In contrast to that paper, in which differentiable potentials of logarithmic type were considered, we investigate here the (more difficult) case of nondifferentiable potentials of double obstacle type. For such nonlinearities, the standard techniques of optimal control theory to establish the existence of Lagrange multipliers for the state constraints are known to fail. To overcome these difficulties, we employ the following line of approach: we use the results contained in the preprint arXiv:1609.07046 [math.AP] (2016), pp. 130, for the case of (differentiable) logarithmic potentials and perform a socalled "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired firstorder necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials. 
P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on nonuniform 1D grids, in: Finite Volumes for Complex Applications VIII  Methods and Theoretical Aspects, FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing AG, Cham, 2017, pp. 303310.

A. Anikin, A. Gasnikov, A. Garinov, P. Dvurechensky, V. Semenov, Parallelizable dual methods for searching equilibriums in largescale mixed traffic assignment problems (in Russian), in: Proceedings of Information Technology and Systems 2016  The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 8589.

A. Chernov, P. Dvurechensky, A primaldual firstorder method for minimization problems with linear constraints, in: Proceedings of Information Technology and Systems 2016  The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 4145.

P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primaldual method for searching equilibrium in hierarchical congestion population games, in: Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016), A. Kononov, I. Bykadorov , O. Khamisov , I. Davydov , P. Kononova , eds., 1623 of CEUR Workshop Proceedings, Technische Universität Aaachen, pp. 584595.

CH. Landry, M. Gerdts, R. Henrion, D. Hömberg, W. Welz, Collisionfree path planning of welding robots, in: Progress in Industrial Mathematics at ECMI 2012, M. Fontes, M. Günther, N. Marheineke, eds., 19 of Mathematics in Industry, Springer, Cham et al., 2014, pp. 251256.

L. Blank, M.H. Farshbaf Shaker, C. Hecht, J. Michl, Ch. Rupprecht, Optimal control of AllenCahn systems, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 1126.

L. Blank, M.H. Farshbaf Shaker, H. Garcke, Ch. Rupprecht, V. Styles, Multimaterial phase field approach to structural topology optimization, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 231246.

T. Bosse, R. Henrion, D. Hömberg, Ch. Landry, H. Leövey ET AL., C2  Nonlinear programming with applications to production processes, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 171187.

C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C  Production, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151153.

M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4  PDEconstrained optimization with industrial applications, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207222.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics  Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227243.

O. Klein, J. Sprekels, SHOWCASE 13  Growth of semiconductor bulk single crystals, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 224225.

CH. Landry, W. Welz, R. Henrion, D. Hömberg, M. Skutella, Task assignment, sequencing and pathplanning in robotic welding cells, Methods and Models in Automation and Robotics (MMAR), 2013  18th International Conference on, Miedzyzdroje, Poland, August 26  29, 2013, IEEE, 2013, pp. 252257.
Abstract
A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and pathplanning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently. 
K. Chełminski, D. Hömberg, O. Rott, Coupling of process, machine, and workpiece in production processes: A challenge for industrial mathematics, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18  19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 5775.

D. Hömberg, D. Kern, PDEconstrained control problems related to the heat treatment of steel, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18  19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 3546.

M.J. Fabian, R. Henrion, A. Kruger, J. Outrata, About error bounds in metric spaces, D. Klatte, H.J. Lüthi, K. Schmedders, eds., Operations Research Proceedings 2011, Springer, Berlin Heidelberg, 2012, pp. 3338.

R. Henrion, Optimization under uncertainty (Models and basic properties), in: Wiley Encyclopedia of Operations Research and Management Science, J.J. Cochran, L.A. Cox, P. Keskinocak ET AL., eds., 5, Wiley, New York, 2011, pp. 33343341.

D. Kern, Die Welt des Herrn Kuhn, in: Besser als Mathe  Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. LutzWestphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 141150.

H. Heitsch, R. Henrion, Ch. Küchler, W. Römisch, Generierung von Szenariobäumen und Szenarioreduktion für stochastische Optimierungsprobleme in der Energiewirtschaft, in: Dezentrale regenerative Energieversorgung: Innovative Modellierung und Optimierung, R. Schultz, H.J. Wagner, eds., LIT Verlag, Münster, 2009, pp. 227254.

D. Hömberg, D. Kern, The heat treatment of steel  A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering  IDE 2008, 1719 September 2008, Bremen, Germany, H.W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201209.

CH. Meyer, D. Hömberg, J. Rehberg, W. Ring, Optimal control of the thermistor problem, in: Optimal Control of Coupled Systems of PDE, Workshop, March 28, 2008, 5 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2008, pp. 624626.

D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl  ein Optimierungsproblem, in: Distortion Engineering  Verzugsbeherrschung in der Fertigung III , 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 3955.

J. Sprekels, D. Tiba, Chapter 18: Optimal Design of Mechanical Structures, in: Control Theory of Partial Differential Equations (proceedings of the conference held at Georgetown University, May 30  June 1, 2003), O. Imanuvilov, G. Leugering, R. Triggiani, B. Zhang, eds., 242 of Lecture Notes in Pure and Applied Mathematics, Chapman & Hall / CRC, Boca Raton, Florida, 2005, pp. 259271.

R. Henrion, Perturbation analysis of chanceconstrained programs under variation of all constraint data, in: Dynamic Stochastic Optimization, K. Marti, ed., 532 of Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg, 2004, pp. 257274.

D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325335.

J. Sprekels, O. Klein, P. Philip, K. Wilmanski, Optimal control of sublimation growth of SiC crystals, in: Mathematics  Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 334343.

J. Sprekels, D. Tiba, Optimization of differential systems with hysteresis, in: Analysis and Optimization of Differential Systems, IFIP TC7/WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 1014, 2002, Constanta, Romania, V. Barbu, I. Lasiecka, D. Tiba, C. Varsan, eds., Kluwer Academic Publishers, Boston, 2003, pp. 387398.

J. Sprekels, D. Tiba, Control variational methods for differential equations, in: Optimal Control of Complex Structures, K.H. Hoffmann, I. Lasiecka, G. Leugering, J.a.T.F. Sprekels, eds., 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, pp. 245257.
Preprints, Reports, Technical Reports

P. Colli, G. Gilardi, E. Rocca, J. Sprekels, Wellposedness and optimal control for a CahnHilliardOono system with control in the mass term, Preprint no. 2867, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2867 .
Abstract, PDF (358 kByte)
The paper treats the problem of optimal distributed control of a CahnHilliardOono system in R^{d}, 1 ≤ d ≤ 3 with the control located in the mass term and admitting general potentials that include both the case of a regular potential and the case of some singular potential. The first part of the paper is concerned with the dependence of the phase variable on the control variable. For this purpose, suitable regularity and continuous dependence results are shown. In particular, in the case of a logarithmic potential, we need to prove an ad hoc strict separation property, and for this reason we have to restrict ourselves to the case d = 2. In the rest of the work, we study the necessary firstorder optimality conditions, which are proved under suitable compatibility conditions on the initial datum of the phase variable and the time derivative of the control, at least in case of potentials having unbounded domain 
P. Colli, A. Signori, J. Sprekels, Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory, Preprint no. 2863, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2863 .
Abstract, PDF (369 kByte)
A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which is a firstorder approximation of a thermodynamically consistent system, is inspired by the theories developed by Green and Naghdi. Two equations, resulting from phase dynamics and the universal balance law for internal energy, are written in terms of the phase variable (representing a nonconserved order parameter) and the socalled thermal displacement, i.e., a primitive with respect to time of temperature. Existence and continuous dependence results are shown for weak and strong solutions to the corresponding initialboundary value problem. Then, an optimal control problem is investigated for a suitable cost functional, in which two data act as controls, namely, the distributed heat source and the initial temperature. Fréchet differentiability between suitable Banach spaces is shown for the controltostate operator, and meaningful firstorder necessary optimality conditions are derived in terms of variational inequalities involving the adjoint variables. Eventually, characterizations of the optimal controls are given. 
P. Colli, A. Signori, J. Sprekels, Optimal control problems with sparsity for phase field tumor growth models involving variational inequalities, Preprint no. 2845, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2845 .
Abstract, PDF (376 kByte)
This paper treats a distributed optimal control problem for a tumor growth model of CahnHilliard type including chemotaxis. The evolution of the tumor fraction is governed by a variational inequality corresponding to a double obstacle nonlinearity occurring in the associated potential. In addition, the control and state variables are nonlinearly coupled and, furthermore, the cost functional contains a nondifferentiable term like the $L^1$norm in order to include sparsity effects which is of utmost relevance, especially time sparsity, in the context of cancer therapies as applying a control to the system reflects in exposing the patient to an intensive medical treatment. To cope with the difficulties originating from the variational inequality in the state system, we employ the socalled “deep quench approximation” in which the convex part of the double obstacle potential is approximated by logarithmic functions. For such functions, firstorder necessary conditions of optimality can be established by invoking recent results. We use these results to derive corresponding optimality conditions also for the double obstacle case, by deducing a variational inequality in terms of the associated adjoint state variables. The resulting variational inequality can be exploited to also obtain sparsity results for the optimal controls. 
M.S. Aronna, J.F. Bonnans, A. Kröner, Stateconstrained controlaffine parabolic problems II: Second order sufficient optimality conditions, Preprint no. 2778, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2778 .
Abstract, PDF (319 kByte)
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear controlstate terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform. 
M. Hintermüller, S.M. Stengl, On the convexity of optimal control problems involving nonlinear PDEs or VIs and applications to Nash games, Preprint no. 2759, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2759 .
Abstract, PDF (381 kByte)
Generalized Nash equilibrium problems in function spaces involving PDEs are considered. One of the central issues arising in this context is the question of existence, which requires the topological characterization of the set of minimizers for each player of the associated Nash game. In this paper, we propose conditions on the operator and the functional that guarantee the reduced formulation to be a convex minimization problem. Subsequently, we generalize results of convex analysis to derive optimality systems also for nonsmooth operators. Our theoretical findings are illustrated by examples. 
A. Alphonse, M. Hintermüller, C.N. Rautenberg, On the differentiability of the minimal and maximal solution maps of elliptic quasivariational inequalities, Preprint no. 2758, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2758 .
Abstract, PDF (259 kByte)
In this short note, we prove that the minimal and maximal solution maps associated to elliptic quasivariational inequalities of obstacle type are directionally differentiable with respect to the forcing term and for directions that are signed. On the way, we show that the minimal and maximal solutions can be seen as monotone limits of solutions of certain variational inequalities and that the aforementioned directional derivatives can also be characterised as the monotone limits of sequences of directional derivatives associated to variational inequalities. 
A. Alphonse, M. Hintermüller, C.N. Rautenberg, Optimal control and directional differentiability for elliptic quasivariational inequalities, Preprint no. 2756, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2756 .
Abstract, PDF (381 kByte)
We focus on elliptic quasivariational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal control of such QVIs. We give three existence theorems based on an order approach, an iteration scheme and a sequential regularisation through partial differential equations. We show that the solution map taking the source term into the set of solutions of the QVI is directionally differentiable for general unsigned data, thereby extending the results of our previous work which provided a first differentiability result for QVIs in infinite dimensions. Optimal control problems with QVI constraints are also considered and we derive various forms of stationarity conditions for control problems, thus supplying among the first such results in this area. 
C. Geiersbach, W. Wollner, Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraint, Preprint no. 2755, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2755 .
Abstract, PDF (321 kByte)
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vectorvalued functions and not only measures. A model problem is given demonstrating the application to PDEconstrained optimization under uncertainty. 
G. Dong, M. Hintermüller, K. Papafitsoros, Optimization with learninginformed differential equation constraints and its applications, Preprint no. 2754, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2754 .
Abstract, PDF (1761 kByte)
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physicsintegrated imaging, differential equation constrained optimization problems with constituents that are only accessible through datadriven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machinelearned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided. 
M. Kantner, Th. Koprucki, Beyond just ``flattening the curve'': Optimal control of epidemics with purely nonpharmaceutical interventions, Preprint no. 2748, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2748 .
Abstract, PDF (3116 kByte)
When effective medical treatment and vaccination are not available, nonpharmaceutical interventions such as social distancing, home quarantine and farreaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptibleexposedinfectiousrecovered) model and continuoustime optimal control theory, we compute the optimal nonpharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of diseaserelated deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socioeconomic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a singleintervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socioeconomic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID19 pandemic in Germany. 
P. Colli, G. Gilardi, J. Sprekels, Optimal control of a phase field system of Caginalp type with fractional operators, Preprint no. 2725, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2725 .
Abstract, PDF (360 kByte)
In their recent work “Wellposedness, regularity and asymptotic analyses for a fractional phase field system” (Asymptot. Anal. 114 (2019), 93128), two of the present authors have studied phase field systems of Caginalp type, which model nonconserved, nonisothermal phase transitions and in which the occurring diffusional operators are given by fractional versions in the spectral sense of unbounded, monotone, selfadjoint, linear operators having compact resolvents. In this paper, we complement this analysis by investigating distributed optimal control problems for such systems. It is shown that the associated controltostate operator is Fréchet differentiable between suitable Banach spaces, and meaningful firstorder necessary optimality conditions are derived in terms of a variational inequality and the associated adjoint state variables. 
M. Eigel, P. Trunschke, R. Schneider, Convergence bounds for empirical nonlinear leastsquares, Preprint no. 2714, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2714 .
Abstract, PDF (4747 kByte)
We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2 norm for which only a weighted Monte Carlo estimate can be computed. The objective is to obtain an approximation of an unknown target function by minimizing the empirical norm. In the case of linear subspaces it is wellknown that such least squares approximations can become inaccurate and unstable when the number of samples is too close to the number of parameters. We review this statement for general nonlinear subsets and establish error bounds for the empirical best approximation error. Our results are based on a restricted isometry property (RIP) which holds in probability and we show sufficient conditions for the RIP to be satisfied with high probability. Several model classes are examined where analytical statements can be made about the RIP. Numerical experiments illustrate some of the obtained stability bounds. 
D. Kamzolov, A. Gasnikov, P. Dvurechensky, On the optimal combination of tensor optimization methods, Preprint no. 2710, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2710 .
Abstract, PDF (284 kByte)
We consider the minimization problem of a sum of a number of functions having Lipshitz p th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain nearoptimal oracle complexity for each function in the sum separately, meaning, in particular, that the oracle for a function with lower Lipschitz constant is called a smaller number of times. As a building block, we extend the current theory of tensor methods and show how to generalize nearoptimal tensor methods to work with inexact tensor step. Further, we investigate the situation when the functions in the sum have Lipschitz derivatives of a different order. For this situation, we propose a generic way to separate the oracle complexity between the parts of the sum. Our method is not optimal, which leads to an open problem of the optimal combination of oracles of a different order. 
F. Stonyakin, A. Gasnikov, A. Tyurin, D. Pasechnyuk, A. Agafonov, P. Dvurechensky, D. Dvinskikh, S. Artamonov, V. Piskunova, Inexact relative smoothness and strong convexity for optimization and variational inequalities by inexact model, Preprint no. 2709, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2709 .
Abstract, PDF (463 kByte)
In this paper we propose a general algorithmic framework for firstorder methods in optimization in a broad sense, including minimization problems, saddlepoint problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, levelset methods, Bregman proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal conditional gradient method and universal method for variational inequalities with composite structure. These method works for smooth and nonsmooth problems with optimal complexity without a priori knowledge of the problem smoothness. As a particular case of our general framework, we introduce relative smoothness for operators and propose an algorithm for VIs with such operator. We also generalize our framework for relatively strongly convex objectives and strongly monotone variational inequalities. 
M. Hintermüller, K. Papafitsoros, C.N. Rautenberg, H. Sun, Dualization and automatic distributed parameter selection of total generalized variation via bilevel optimization, Preprint no. 2689, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2689 .
Abstract, PDF (25 MByte)
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first and secondorder derivatives. This helps to avoid the staircasing effect of Total Variation (TV) regularization, while still preserving sharp contrasts in images. The associated regularization effect crucially hinges on two parameters whose proper adjustment represents a challenging task. In this work, a bilevel optimization framework with a suitable statisticsbased upper level objective is proposed in order to automatically select these parameters. The framework allows for spatially varying parameters, thus enabling better recovery in highdetail image areas. A rigorous dualization framework is established, and for the numerical solution, two Newton type methods for the solution of the lower level problem, i.e. the image reconstruction problem, and two bilevel TGV algorithms are introduced, respectively. Denoising tests confirm that automatically selected distributed regularization parameters lead in general to improved reconstructions when compared to results for scalar parameters. 
D. Gahururu, M. Hintermüller, S.M. Stengl, Th.M. Surowiec, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion, Preprint no. 2654, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2654 .
Abstract, PDF (337 kByte)
PDEconstrained (generalized) Nash equilibrium problems (GNEPs) are considered in a deterministic setting as well as under uncertainty. This includes a study of deterministic GNEPs with nonlinear and/or multivalued operator equations as forward problems and PDEconstrained GNEPs with uncertain data. The deterministic nonlinear problems are analyzed using the theory of generalized convexity for setvalued operators, and a variational approximation approach is proposed. The stochastic setting includes a detailed overview of the recently developed theory and algorithms for riskaverse PDEconstrained optimization problems. These new results open the way to a rigorous study of stochastic PDEconstrained GNEPs. 
M. EbelingRump, D. Hömberg, R. Lasarzik, Th. Petzold, Topology optimization subject to additive manufacturing constraints, Preprint no. 2629, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2629 .
Abstract, PDF (1099 kByte)
In Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a GinzburgLandau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an AllenCahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem. 
C. Grässle, M. Hintermüller, M. Hinze, T. Keil, Simulation and control of a nonsmooth CahnHilliard NavierStokes system with variable fluid densities, Preprint no. 2617, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2617 .
Abstract, PDF (11 MByte)
We are concerned with the simulation and control of a two phase flow model governed by a coupled CahnHilliard NavierStokes system involving a nonsmooth energy potential.We establish the existence of optimal solutions and present two distinct approaches to derive suitable stationarity conditions for the bilevel problem, namely C and strong stationarity. Moreover, we demonstrate the numerical realization of these concepts at the hands of two adaptive solution algorithms relying on a specifically developed goaloriented error estimator.In addition, we present a model order reduction approach using proper orthogonal decomposition (PODMOR) in order to replace highfidelity models by low order surrogates. In particular, we combine POD with spaceadapted snapshots and address the challenges which are the consideration of snapshots with different spatial resolutions and the conservation of a solenoidal property.
Vorträge, Poster

A. Alphonse, Directional differentiability and optimal control for elliptic quasivariational inequalities, Workshop ``Challenges in Optimization with Complex PDESystems'' (Online Workshop), February 14  20, 2021, Mathematisches Forschungsinstitut Oberwolfach, February 17, 2021.

A. Alphonse, Directional differentiability and optimal control for elliptic quasivariational inequalities (online talk), Meeting of the Scientific Advisory Board of WIAS, WIAS Berlin, March 12, 2021.

A. Alphonse, Some aspects of sensitivity analysis and optimal control for elliptic QVIs (coauthors: Michael Hintermüller and Carlos Rautenberg, online talk), 91th Annual Meeting of the International Association of Applied Mathematics and Mechanics (Online Event), Session DFGPP 1962 Nonsmooth and Complementaritybased Distributed Parameter Systems, March 15  19, 2021, Universität Kassel, March 16, 2021.

A. Alphonse, Some aspects of sensitivity analysis and optimal control for elliptic QVIs (online talk), Annual Meeting of the DFG SPP 1962 (Virtual Conference), March 24  25, 2021, WIAS Berlin, March 25, 2021.

P. Farrell, Modelling and simulation of the lateral photovoltage scanning method (online talk), European Conference on Mathematics for Industry (ECMI2021), MSOEE: Mathematical modeling of charge transport in graphene and low dimensional structures (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, Hungary, April 13, 2021.

D. Sommer, Robust nonlinear model predictive control using tensor networks (online talk), European Conference on Mathematics for Industry (ECMI2021), MS23: DataDriven Optimization (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 14, 2021.

C. Geiersbach, Almost sure state constraints with an application to stochastic Nash equilibrium problems, SIAM Conference on Computational Science and Engineering  CSE21 (Virtual Conference), Minisymposium MS 114 ``RiskAverse PDEConstrained Optimization'', March 1  5, 2021, Virtual Conference Host: National Security Agency (NSA), March 2, 2021.

C. Geiersbach, Optimality conditions and regularization for convex stochastic optimization with almost sure state constraints, Workshop ``Challenges in Optimization with Complex PDESystems'' (Online Workshop), February 14  20, 2021, Mathematisches Forschungsinstitut Oberwolfach, February 16, 2021.

C. Geiersbach, Stochastic Approximation for Optimization in Shape Spaces (part of the minisymposium 'UQ in free boundary problems'  Helmut Harbrecht), 15th International Conference on Free Boundary Problems: Theory and Applications (online), Weierstrass Institute, September 14, 2021.

C. Geiersbach, Stochastic approximation for optimization in shape spaces, 15th International Conference on Free Boundary Problems: Theory and Applications 2021 (FBP 2021, Online Event), Minisymposium ``UQ in Free Boundary Problems'', September 13  17, 2021, WIAS, Berlin, September 14, 2021.

C. Geiersbach, Stochastic approximation with applications to PDEconstrained optimization under uncertainty (online talk), WIAS Seminar ``Modern Methods in Applied Stochastics and Nonparametric Statistics'', March 9, 2021.

C. Geiersbach, Stochastic approximation with applications to PDEconstrained optimization under uncertainty  Part two (online talk), WIAS Seminar ``Modern Methods in Applied Stochastics and Nonparametric Statistics'', April 20, 2021.

M. EbelingRump, Topology optimization subject to a local volume constraint (online talk), European Conference on Mathematics for Industry (ECMI2021), MS07: Maths for the Digital Factory (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 15, 2021.

M. Hintermüller, Non smooth and complementaritybased distributed parameter systems: Simulation and hierarchical optimization (online talk), 91th Annual Meeting of the International Association of Applied Mathematics and Mechanics (Online Event), Session DFGPP 1962 Nonsmooth and Complementaritybased Distributed Parameter Systems, March 15  19, 2021, Universität Kassel, March 16, 2021.

M. Hintermüller, Optimal control of quasivariational inequalities (online talk), SIAM Conference on Optimization (OP21) (Online Event), Minisymposium MS93 ``Nonsmooth Problems and Methods in Largescale Optimization'', July 20  23, 2021, July 23, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications, Online Conference ``Industrial and Applied Mathematics'', January 11  15, 2021, The Hong Kong University of Science and Technology, Institute for Advanced Study, January 13, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications (online talk), INdAM Workshop 2021: ``Analysis and Numerics of Design, Control and Inverse Problems'' (Online Event), July 1  7, 2021, Istituto Nazionale di Alta Matematica, Rome, Italy, July 5, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications (online talk), Deep Learning and Inverse Problems (MDLW02), September 27  October 1, 2021, Isaac Newton Institute for Mathematical Sciences (Hybrid Event), Oxford, UK, October 1, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications (online talk), Seminar CMAI, George Mason University, Center for Mathematics and Artificial Intelligence, Fairfax, USA, March 19, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications (online talk), One World Optimization Seminar, Universität Wien, Fakultät für Mathematik, Austria, May 10, 2021.

M. Hintermüller, Semismooth Newton methods: Theory, numerical algorithms and applications I (online talk), International Forum on Frontiers of Intelligent Medical Image Analysis and Computing 2021 (Online Forum), Xidian University, Southeastern University, and Hong Kong Baptist University, China, July 19, 2021.

M. Hintermüller, Semismooth Newton methods: Theory, numerical algorithms and applications II (online talk), International Forum on Frontiers of Intelligent Medical Image Analysis and Computing 2021 (Online Forum), Xidian University, Southeastern University, and Hong Kong Baptist University, China, July 26, 2021.

D. Hömberg, Modelling and simulation of highfrequency induction welding (online talk), European Conference on Mathematics for Industry (ECMI2021), MS08: Modelling Simulation and Optimization in Electrical Engineering (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 13, 2021.

M. Kantner, Mathematical modeling and optimal control of the COVID19 pandemic (online talk), Mathematisches Kolloquium, Bergische Universität Wuppertal, April 27, 2021.

K. Papafitsoros, Optimization with learninginformed differential equation constraints and its applications (online talk), University of Graz, Institute of Mathematics and Scientific Computing, January 21, 2021.

K. Papafitsoros, Optimization with learninginformed differential equation constraints and its applications (online talk), Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics, WIAS Berlin, March 16, 2021.

G. Dong, Integrated physicsbased method, learninginformed model and hyperbolic PDEs for imaging, Efficient Algorithms in Data Science, Learning and Computational Physics, Sanya, China, January 12  16, 2020.

M. Hintermüller, Functionalanalytic and numerical issues in splitting methods for total variationbased image reconstruction, The Fifth International Conference on Numerical Analysis and Optimization, January 6  9, 2020, Sultan Qaboos University, Oman, January 6, 2020.

M. Hintermüller, Magnetic resonance fingerprinting of integrated physics models, Efficient Algorithms in Data Science, Learning and Computational Physics, January 12  16, 2020, Sanya, China, January 15, 2020.

D. Hömberg, Maths for the digital factory (online talk), Workshop on Industrial Mathematics and Computer Science (Online Event), University of Craiova, Romania, October 31, 2020.

A. Kröner, Optimal control of a semilinear heat equation subject to state and control constraints, Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization, WIAS, February 27, 2020.

K. Papafitsoros, Automatic distributed regularization parameter selection in Total Generalized Variation image reconstruction via bilevel optimization, Seminar, Southern University of Science and Technology, Shenzhen, China, January 17, 2020.

K. Papafitsoros, Automatic distributed regularization parameter selection in Total Generalized Variation image reconstruction via bilevel optimization, Seminar, Shenzhen MSUBIT University, Department of Mathematics, Shenzhen, China, January 16, 2020.

K. Papafitsoros, Automatic distributed regularization parameter selection in imaging via bilevel optimization, Workshop on PDE Constrained Optimization under Uncertainty and Mean Field Games, January 28  30, 2020, WIAS, Berlin, January 30, 2020.

K. Papafitsoros, Spatially dependent parameter selection in TGV based image restoration via bilevel optimization, Efficient Algorithms in Data Science, Learning and Computational Physics, Sanya, China, January 12  16, 2020.

A. Alphonse, Directional differentiability for elliptic quasivariational inequalities, Workshop ``Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, Stochastic, Nonlocal and Discrete Structures'', January 20  26, 2019, Mathematisches Forschungsinstitut Oberwolfach, January 25, 2019.

A. Alphonse, Directional differentiability for elliptic quasivariational inequalities, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Best Paper Session, August 5  8, 2019, Berlin, August 5, 2019.

H. Heitsch, Optimal Neumann boundary control of the vibrating string with uncertain initial data and probabilistic terminal constraints, The XV International Conference on Stochastic Programming (ICSP XV), Minisymposium ``Nonlinear Programming with Probability Functions'', July 29  August 2, 2019, Norwegian University of Science and Technology, Trondheim, Norway, July 30, 2019.

T. Keil, Optimal control of a coupled CahnHilliardNavierStokes system with variable fluid densities, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Session ``Optimal Control of Phase Field Models'', August 5  8, 2019, Berlin, August 5, 2019.

S.M. Stengl, M. Hintermüller, On the convexity of optimal control problems involving nonlinear PDEs or VIs, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Berlin, August 5  8, 2019.

S.M. Stengl, On the convexity of optimal control problems involving nonlinear PDEs or VIs, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Session ``QuasiVariational Inequalities and Generalized Nash Equilibrium Problems (Part I)'', August 5  8, 2019, Berlin, August 6, 2019.

C. Löbhard, Spacetime discretization for parabolic optimal control problems with state constraints, ICCOPT 2019  Sixth International Conference on Continuos Optimization, Session ``Optimal Control and Dynamical Systems (Part VI)'', August 5  8, 2019, Berlin, August 7, 2019.

R. Sandilya, Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Session ``QuasiVariational Inequalities and Generalized Nash Equilibrium Problems (Part II)'', August 5  8, 2019, Berlin, August 7, 2019.

M. EbelingRump, Topology optimization subject to additive manufacturing constraints, INdAM Workshop MACH2019 ``Mathematical Modeling and Analysis of Degradation and Restoration in Cultural Heritage'', March 25  29, 2019, Istituto Nazionale di Alta Matematica ``Francesco Severi'', Rome, Italy, March 26, 2019.

M. EbelingRump, Topology optimization subject to additive manufacturing constraints, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Session ``InfiniteDimensional Optimization of Nonlinear Systems (Part III)'', August 5  8, 2019, Berlin, August 6, 2019.

R. Henrion, Nonsmoothness in the context of probability functions, Workshop 4 within the Special Semester on Optimization ``Nonsmooth Optimization'', November 25  27, 2019, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 25, 2019.

R. Henrion, On some extended models of chance constraints, Workshop ``Mathematical Optimization of Systems Impacted by Rare, HighImpact Random Events'', June 24  28, 2019, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, USA, June 24, 2019.

R. Henrion, Optimal Neumann boundary control of the vibrating string under random initial conditions, OVA9: 9th International Seminar on Optimization and Variational Analysis, Universidad Miguel Hernández, Elche, Spain, September 2, 2019.

R. Henrion, Optimal Neumann boundary control of the vibrating string with uncertain initial data, ICCOPT 2019  Sixth International Conference on Continuous Optimization, Session ``PDEconstrained Optimization under Uncertainty (Part I)'', August 5  8, 2019, Berlin, August 8, 2019.

R. Henrion, Optimal probabilistic control of the vibrating string under random initial conditions, PGMO DAYS 2018, Session 1E ``Stochastic Optimal Control'', December 3  4, 2019, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF'Lab ParisSaclay, Palaiseau, France, December 4, 2019.

R. Henrion, Probabilistic constraints in optimization with PDEs, Workshop 3 within the Special Semester on Optimization ``Optimization and Inversion under Uncertainty'', November 11  15, 2019, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 13, 2019.

R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Spring School in Nonsmooth Analysis and Optimization, April 16  18, 2019, Université Mohammed V, Rabat, Morocco.

R. Henrion, Robust control of a sweeping process with probabilistic endpoint constraints, The XV International Conference on Stochastic Programming (ICSP XV), Minisymposium ``Nonlinear Programming with Probability Functions'', July 29  August 2, 2019, Norwegian University of Science and Technology, Trondheim, Norway, July 30, 2019.

M. Hintermüller, Generalized Nash equilibrium problems with PDEs connected to spot markets with (gas) transport, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Session MS ME14 1 ``Recent Advances in PDEconstrained Optimization'', July 15  19, 2019, Valencia, Spain, July 15, 2019.

M. Hintermüller, Generalized Nash equilibrium problems with application to spot markets with gas transport, Workshop ``Electricity Systems of the Future: Incentives, Regulation and Analysis for Efficient Investment'', March 18  22, 2019, Isaac Newton Institute, Cambridge, UK, March 21, 2019.

M. Hintermüller, Generalized Nash games with PDEs and applications in energy markets, FrenchGermanSwiss Conference on Optimization (FGS'2019), September 17  20, 2019, Nice, France, September 20, 2019.

M. Hintermüller, Lecture Series: Optimal control of nonsmooth structures, Thematic Programme ``Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions'', February 4  7, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Colloquium of the Mathematical Institute, University of Oxford, UK, June 7, 2019.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland, December 3, 2019.

M. Hintermüller, Optimal control problems involving nonsmooth structures, Autumn School 2019 ``Optimal Control and Optimization with PDEs'' (ALOP), October 7  10, 2019, Universität Trier.

R. Lasarzik, Optimal control via relative energies, Workshop ``Recent Trends in Optimal Control of Partial Differential Equations'', February 25  27, 2019, Technische Universität Berlin, February 27, 2019.

R. Lasarzik, Weak entropic solutions to a model in induction hardening: Existence and weakstrong uniqueness, Decima Giornata di Studio Università di Pavia  Politecnico di Milano Equazioni Differenziali e Calcolo delle Variazioni, Politecnico di Milano, Italy, February 21, 2019.

R. Lasarzik, Weak entropy solutions in the context of induction hardening, 9th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium CP FT17 9 ``Partial Differential Equations VII'', July 15  19, 2019, Valencia, Spain, July 19, 2019.

C.N. Rautenberg, A nonlocal variational model in image processing associated to the spatially variable fractional Laplacian, ICCOPT 2019  Sixth International Conference on Continuous Optimization, August 5  8, 2019, Berlin, August 6, 2019.

C.N. Rautenberg, Parabolic quasivariational inequalities with gradient and obstacle type constraints, Thematic Programme ``Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions'', January 28  February 1, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, January 31, 2019.

N. Alia, Modeling and optimization of a gasstirred liquid flow for steelmaking processes, The 20th European Conference on Mathematics for Industry (ECMI), MS27: MSO for steel production and manufacturing, June 18  22, 2018, University Budapest, Institute of Mathematics at Eötvös Loránd, Hungary, June 19, 2018.

A. Alphonse, Optimal Control of Elliptic and Parabolic QuasiVariational Inequalities, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), October 3, 2018.

A. Alphonse, Parabolic quasivariational inequalities: Existence and sensitivity analysis, 4th Central European SetValued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, PhilippsUniversität Marburg, November 24, 2018.

A. Alphonse, Directional differentiability for elliptic QVIs of obstacle type, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19  23, 2018, Technische Universität München, March 20, 2018.

A. Alphonse, Directional differentiability for elliptic quasivariational inequalities, Workshop ``Challenges in Optimal Control of Nonlinear PDESystems'', April 8  14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 12, 2018.

M.J. Arenas Jaén, Modelling, simulation and optimization of inductive preheating for thermal cutting of steel plates, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18  22, 2018, Budapest, Hungary, June 19, 2018.

L. Capone, Induction hardening of cam profiles: Modeling, simulation, and optimization, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18  22, 2018, Budapest, Hungary, June 19, 2018.

T. Keil, Simulation and Control of a Nonsmooth CahnHilliardNavierStokes System with Variable Fluid Densities, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), Germany, October 2, 2018.

T. Keil, Strong stationarity conditions for the optimal control of a CahnHilliardNavierStokes system, 5th European Conference on Computational Optimization, Session ``Infinite Dimensional Nonsmooth Optimization'', September 10  12, 2018, Trier, September 12, 2018.

S.M. Stengl, Generalized Nash equilibrium problems with partial differential operators: theory, algorithms and risk aversion, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), October 1, 2018.

C. Löbhard, Analysis, algorithms and applications for the optimal control of variational inequalities, European Women in Mathematics (EWM) General Meeting 2018, Minisymposium 9 ``Nonsmooth PDEconstrained Optimization: Problems and Methods'', September 3  7, 2018, KarlFranzensUniversität Graz, Austria, September 7, 2018.

C. Löbhard, Optimal shape design of air ducts in combustion engines, ROMSOC MidTerm Meeting, November 26  27, 2018, Universität Bremen, November 26, 2018.

P. Dvurechensky, Computational optimal transport: Accelerated gradient descent vs Sinkhorn, ISMP 2018 Bordeaux, July 1  6, 2018, University of Bordeaux, Institut de Mathématiques, France, July 4, 2018.

P. Dvurechensky, Computational optimal transport: Accelerated gradient descent vs. Sinkhorn's algorithm, Statistical Optimal Transport, July 24  25, 2018, Skolkovo Institute of Science and Technology, Moscow, Russian Federation, July 25, 2018.

P. Dvurechensky, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, The 35th International Conference on Machine Learning (ICML 2018), Stockholm, Sweden, July 9  15, 2018.

P. Dvurechensky, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, The 35th International Conference on Machine Learning (ICML 2018), July 9  15, 2018, International Machine Learning Society (IMLS), Stockholm, Sweden, July 11, 2018.

P. Dvurechensky, Faster algorithms for (regularized) optimal transport, Grenoble Optimization Days 2018, June 28  29, 2018, Université Grenoble Alpes, Laboratoire Jean Kuntzmann, France, June 29, 2018.

P. Dvurechensky, Primaldual methods for solving infinitedimensional games, Games, Dynamics and Optimization GDO2018, March 13  15, 2018, Universität Wien, Fakultät für Mathematik, Austria, March 15, 2018.

R. Henrion, Dynamic chance constraints under continuous random distribution, PGMO DAYS 2018, Session 1E ``Stochastic Optimization'', November 20  21, 2018, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF'Lab ParisSaclay, Palaiseau, France, November 21, 2018.

R. Henrion, Lipschitz properties and their moduli for constraint mappings, 4th Central European SetValued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, PhilippsUniversität Marburg, November 24, 2018.

R. Henrion, Mstationary conditions for MPECs in finite dimension (Part 1+2), SPP 1962 Summer School on Complementarity Problems in Applied Mathematics: Modeling, Analysis, and Optimization, July 30  August 1, 2018, Technische Universität Dortmund, July 31, 2018.

R. Henrion, Optimization problems under probabilistic constraints, 3rd RussianGerman Conference on MultiScale BioMathematics: Coherent Modeling of Human Body System, November 7  9, 2018, Lomonosov Moscow State University, Russian Federation, November 8, 2018.

R. Henrion, Perspectives in probabilistic programming under continuous random distributions, Workshop ``New Directions in Stochastic Optimisation'', August 19  25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 20, 2018.

R. Henrion, Verification and comparison of the calmness of generalized equations in original and enhanced form, International Workshop on Optimization and Variational Analysis, January 10  11, 2018, Termas de Cauquenes, Chile, January 11, 2018.

M. Hintermüller, Automated regularization parameter choice rule in image processing, Workshop ``New Directions in Stochastic Optimisation'', August 19  25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 23, 2018.

M. Hintermüller, Bilevel optimization and some "parameter learning" applications in image processing, SIAM Conference on Imaging Science, Minisymposium MS5 ``Learning and Adaptive Approaches in Image Processing'', June 5  8, 2018, Bologna, Italy, June 5, 2018.

M. Hintermüller, Generalised Nash equilibrium problems with partial differential equations, Search Based Model Engineering Workshop, August 7  9, 2018, King's College London, UK, August 7, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, International Workshop on PDEConstrained Optimization, Optimal Controls and Applications, December 10  14, 2018, Sanya, China, December 13, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, 23rd International Symposium on Mathematical Programming (ISMP2018), July 1  6, 2018, Bordeaux, France, July 2, 2018.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Mathematisches Kolloquium, Universität Bielefeld, Fakultät für Mathematik, June 7, 2018.

M. Hintermüller, Recent advances in nonsmooth and complementaritybased distributed parameter systems, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19  23, 2018, Technische Universität München, March 20, 2018.

M. Hintermüller, Semismooth Newton methods in PDE constrained optimization, Advanced Training in Mathematics Schools ``New Directions in PDE Constrained Optimisation'', March 12  16, 2018, National Centre for Mathematics of IIT Bombay and TIFR, Mumbai, Bombay, India.

R. Lasarzik, Generalized solution concepts to the EricksenLeslie equations modeling liquid crystal flow, 28th IFIP TC 7 Conference on System Modelling and Optimization, July 23  27, 2018, Universität DuisburgEssen, Essen, July 26, 2018.

C.N. Rautenberg, On the optimal control of quasivariational inequalities, 23rd International Symposium on Mathematical Programming (ISMP2018), Session 221 ``Optimization Methods for PDE Constrained Problems'', July 1  6, 2018, Bordeaux, France, July 3, 2018.

C.N. Rautenberg, Optimization problems with quasivariational inequality constraints, Workshop ``Challenges in Optimal Control of Nonlinear PDESystems'', April 8  14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 11, 2018.

C.N. Rautenberg, Spatially distributed parameter selection in Total Variation (TV) models, MIA 2018  Mathematics and Image Analysis, HumboldtUniversität zu Berlin, January 15  17, 2018.

C.N. Rautenberg, Evolutionary quasivariational inequalities: Applications, theory, and numerics, 5th International Conference on Applied Mathematics, Design and Control: Mathematical Methods and Modeling in Engineering and Life Sciences, November 7  9, 2018, San Martin National University, Buenos Aires, Argentina, November 9, 2018.

A. Alphonse, Optimal control of elliptic and parabolic quasivariational inequalities, Annual Meeting of the DFG Priority Programme 1962, October 9  11, 2017, Kremmen (Sommerfeld), October 10, 2017.

T. Keil, Simulation and control of a nonsmooth CahnHilliard NavierStokes system with variable fluid densities (with Carmen Graessle), Annual Meeting of the DFG Priority Programme 1962, October 9  11, 2017, Kremmen (Sommerfeld), October 11, 2017.

T. Keil, Strong stationarity conditions for the optimal control of a CahnHilliardNavierStokes system, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9  14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

S.M. Stengl, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms and risk aversion (with Deborah Gahururu), Annual Meeting of the DFG Priority Programme 1962, October 9  11, 2017, Kremmen (Sommerfeld), October 9, 2017.

J. Sprekels, Optimal control of PDEs: From basic principles to hard applications, International School ``Frontiers in Partial Differential Equations and Solvers'', May 22  25, 2017, University of Pavia, Department of Mathematics, Italy.

C. Löbhard, A function space based solution method with spacetime adaptivity for parabolic optimal control problems with state constraints, PGMO Days 2017, November 13  14, 2017, EDF Lab Paris Saclay, France, November 14, 2017.

C. Löbhard, An adaptive spacetime discretization for parabolic optimal control problem with state constraints, Joint Research Seminar on Mathematical Optimization / Nonsmooth Variational Problems and Operator Equations, WIAS, Berlin, June 22, 2017.

C. Löbhard, An ddaptive discontinuous Galerkin method for a parabolic optimal control problem with state constraints . . ., Workshop on Optimization of Infinite Dimensional NonSmooth Distributed Parameter Systems, October 4  6, 2017, Darmstadt, October 4, 2017.

C. Löbhard, Spacetime discretization of a parabolic optimal control problem with state constraints, 18th FrenchGermanItalian Conference on Optimization, September 25  28, 2017, Paderborn, September 26, 2017.

P. Dvurechensky, Adaptive similar triangles method: A stable alternative to Sinkhorn's algorithm for regularized optimal transport, CoEvolution of Nature and Society Modelling, Problems & Experience. Devoted to Academician Nikita Moiseev centenary (Moiseev100)., November 7  10, 2017, Russian Academy of Science, Federal Research Center Computer Science and Control, Moskau, Russian Federation, November 9, 2017.

P. Dvurechensky, Faster algorithms for optimal transport, 3. International Matheon Conference on Compressed Sensing and its Applications 2017, Berlin, December 4  8, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite nonconvex optimization, Optimization and Statistical Learning, Les Houches, France, April 10  14, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite nonconvex optimization, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 17  19, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite nonconvex optimization, 18th French  German  Italian Conference on Optimization, September 25  28, 2017, Universität Paderborn, Fakultät für Elektrotechnik, Informatik und Mathematik, Paderborn, September 27, 2017.

P. Dvurechensky, Gradient method with inexact oracle for non convex optimization, 3rd Applied Mathematics Symposium Münster: Shape, Imaging and Optimization, February 28  March 3, 2017.

R. Henrion, A friendly tour through the world of calmness, 11th International Conference on Parametric Optimization and Related Topics (ParaoptXI), September 19  22, 2017, Prague, Czech Republic, September 19, 2017.

R. Henrion, Comparing and verifying calmness conditions for MPECs, Second Workshop on Metric Bounds and Transversality (WoMBaT 2017), November 30  December 2, 2017, RMIT University, Melbourne, Australia, November 30, 2017.

R. Henrion, Contraintes en probabilité: Formules du gradient et applications, Workshop ``MASMODE 2017'', Institut Henri Poincaré, Paris, France, January 9, 2017.

R. Henrion, On Mstationary condition for a simple electricity spot market model, Workshop ``Variational Analysis and Applications for Modelling of Energy Exchange'', May 4  5, 2017, Université Perpignan, France, May 4, 2017.

R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Université de Bourgogne, Département de Mathématiques, Dijon, France, October 25, 2017.

M. Hintermüller, (Pre)Dualization, dense embeddings of convex sets, and applications in image processing, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, International Center for Mathematics, University of Lisbon, Portugal, December 6, 2017.

M. Hintermüller, (Pre)Dualization, dense embeddings of convex sets, and applications in image processing, HCM Workshop: Nonsmooth Optimization and its Applications, May 15  19, 2017, Hausdorff Center for Mathematics, Bonn, May 15, 2017.

M. Hintermüller, Adaptive finite element solvers for MPECs in function space, SIAM Conference on Optimization, Minisymposium MS122 ``Recent Trends in PDEConstrained Optimization'', May 22  25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

M. Hintermüller, Bilevel optimization and applications in imaging, Workshop ``Emerging Developments in Interfaces and Free Boundaries'', January 22  28, 2017, Mathematisches Forschungsinstitut Oberwolfach.

M. Hintermüller, Bilevel optimization and applications in imaging, Mathematisches Kolloquium, Universität Wien, Austria, January 18, 2017.

M. Hintermüller, Bilevel optimization and some ``parameter learning'' applications in image processing, LMS Workshop ``Variational Methods Meet Machine Learning'', September 18, 2017, University of Cambridge, Centre for Mathematical Sciences, UK, September 18, 2017.

M. Hintermüller, Generalized Nash equilibrium problems in Banach spaces: Theory, NikaidoIsodabased pathfollowing methods, and applications, The Third International Conference on Engineering and Computational Mathematics (ECM2017), Stream 3 ``Computational Optimization'', May 31  June 2, 2017, The Hong Kong Polytechnic University, China, June 2, 2017.

M. Hintermüller, Generalized Nash games with partial differential equations, Kolloquium Arbeitsgruppe Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, June 20, 2017.

M. Hintermüller, Nonsmooth structures in PDEconstrained optimization, Mathematisches Kolloquium, Universität DuisburgEssen, Fakultät für Mathematik, Essen, January 11, 2017.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Optimization Seminar, Chinese Academy of Sciences, State Key Laboratory of Scientific and Engineering Computing, Beijing, China, June 6, 2017.

M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, Seminar, Isaac Newton Institute, Programme ``Variational Methods and Effective Algorithms for Imaging and Vision'', Cambridge, UK, August 30, 2017.

M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, University College London, Centre for Inverse Problems, UK, October 27, 2017.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Kolloquium, FriedrichAlexanderUniversität ErlangenNürnberg, Department Mathematik, Erlangen, May 2, 2017.

M. Hintermüller, Optimal control of multiphase fluids based on non smooth models, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9  14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

M. Hintermüller, Optimal control of nonsmooth phasefield models, DFGAIMS Workshop on ``Shape Optimization, Homogenization and Control'', March 13  16, 2017, Mbour, Senegal, March 14, 2017.

M. Hintermüller, Recent trends in PDEconstrained optimization with nonsmooth structures, Fourth Conference on Numerical Analysis and Optimization (NAOIV2017), January 2  5, 2017, Sultan Qaboos University, Muscat, Oman, January 4, 2017.

M. Hintermüller, Total variation diminishing RungeKutta methods for the optimal control of conservation laws: Stability and orderconditions, SIAM Conference on Optimization, Minisymposium MS111 ``Optimization with Balance Laws on Graphs'', May 22  25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

D. Hömberg, European collaboration in industrial and applied mathematics, 25th Conference on Applied and Industrial Mathematics (CAIM), September 14  17, 2017, University of Iaşi, Romania, September 14, 2017.

D. Hömberg, From dilatometer experiments to distortion compensation  Optimal control problems related to solidsolid phase transitions, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway, November 3, 2017.

D. Hömberg, MSO for steel production and manufacturing, Workshop ``Future and Emerging Mathematical Technologies in Europe'', December 11  15, 2017, Lorentz Center, Leiden, Netherlands, December 11, 2017.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, The 15th Annual Meeting of the China Society for Industrial and Applied Mathematics, Embedded Meeting EM02 ``A3 Workshop on Modeling and Computation of Applied Inverse Problems'', October 12  15, 2017, Qingdao, China, October 14, 2017.

J. Neumann, The phase field approach for topology optimization under uncertainties, ZIB Computational Medicine and Numerical Mathematics Seminar, KonradZuseZentrum für Informationstechnik Berlin, August 25, 2016.

TH. Petzold, The MIMESIS project  An example for an interdisciplinary research project, LeibnizKolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9  11, 2016, LeibnizGemeinschaft, Berlin, November 9, 2016.

P. Dvurechensky, Accelerated primaldual gradient method for composite optimization with unknown smoothness parameter, VIII Moscow International Conference on Operations Research (ORM2016), November 18  21, 2016, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation, October 19, 2016.

P. Dvurechensky, Accelerated primaldual gradient method for linearly constrained minimization Problems, VII International Conference Optimization and Applications, September 25  28, 2016, Montenegrin Academy of Sciences and Arts, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Sciences, University of Evora, Portugal, Moscow Institute of Physics and Technology, Russiate of Physics and Technology, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Science, Petrovac, Montenegro, September 26, 2016.

M.H. Farshbaf Shaker, A phase field approach for optimal boundary control of damage processes in twodimensional viscoelastic media, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20  24, 2016, Cortona, Italy, June 21, 2016.

M.H. Farshbaf Shaker, AllenCahn MPECs, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10  12, 2016, WIAS Berlin, May 11, 2016.

S.P. Frigeri, On some nonlocal diffuseinterface models for binary fluids: Regularity results and applications, Congress of the Italian Society of Industrial and Applied Mathematics (SIMAI 2016), September 13  16, 2016, Politecnico di Milano, Italy, September 14, 2016.

S.P. Frigeri, Optimal distributed control for nonlocal CahnHilliard/NavierStokes systems in 2D, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20  24, 2016, Cortona, Italy, June 24, 2016.

R. Henrion, Aspects of nondifferentiability for probability functions, 7th International Seminar on Optimization and Variational Analysis, June 1  3, 2016, Universidad de Alicante, Spain, June 2, 2016.

R. Henrion, Aspects of nonsmoothness for Gaussian probability functions, PGMO Days 2016  Gaspard Monge Program for Optimization and Operations Research, November 8  9, 2016, Electricité de France, Palaiseau, France, November 9, 2016.

R. Henrion, Calmness of the perturbation mappings for MPECs in original and enhanced form, International Conference on Bilevel Optimization and Related Topics, May 4  6, 2016, Dresden, May 6, 2016.

M. Hintermüller, S. Hajian, N. Strogies, Subproject B02  Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Annual Meeting of the Collaborative Research Center/Transregio (TRR) 154 ``Mathematical Modeling, Simulation and Optimization Using the Example of Gas Networks'', Technische Universität Berlin, October 4  5, 2016.

M. Hintermüller, S. Hajian, N. Strogies, Subproject B02  Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Conference ``Mathematics of Gas Transport'', KonradZuseZentrum für Informationstechnik Berlin, October 6  7, 2016.

M. Hintermüller, Adaptive finite elements in total variation based image denoising, SIAM Conference on Imaging Science, Minisymposium ``Leveraging Ideas from Imaging Science in PDEconstrained Optimization'', May 23  26, 2016, Albuquerque, USA, May 24, 2016.

M. Hintermüller, Bilevel optimization for a generalized totalvariation model, SIAM Conference on Imaging Science, Minisymposium ``NonConvex Regularization Methods in Image Restoration'', May 23  26, 2016, Albuquerque, USA, May 26, 2016.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, 66th Workshop ``Advances in Convex Analysis and Optimization'', July 5  10, 2016, International Centre for Scientific Culture ``E. Majorana'', School of Mathematics ``G. Stampacchia'', Erice, Italy, July 9, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10  12, 2016, WIAS Berlin, May 11, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, The Fifth International Conference on Continuous Optimization, Session: ``Recent Developments in PDEconstrained Optimization I'', August 6  11, 2016, Tokyo, Japan, August 10, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, June 9, 2016.

M. Hintermüller, Optimal selection of the regularisation function in a localised TV model, SIAM Conference on Imaging Science, Minisymposium ``Analysis and Parameterisation of Derivative Based Regularisation'', May 23  26, 2016, Albuquerque, USA, May 24, 2016.

M. Hintermüller, Recent trends in optimal control problems with nonsmooth structures, Computational Methods for Control of Infinitedimensional Systems, March 14  18, 2016, Institute for Mathematics and its Applications, Minneapolis, USA, March 14, 2016.

M. Hintermüller, Towards sharp stationarity conditions for classes of optimal control problems for variational inequalities of the second kind, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20  24, 2016, Cortona, Italy, June 20, 2016.

D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

D. Hömberg, Math for steel production and manufacturing, MACSI10  Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8  9, 2016, University of Limerick, Ireland, December 9, 2016.

M. Eigel, Reliable averaging for the primal variable in the courant FEM and hierarchical error estimators on redrefined meshes, 28th Chemnitz FEM Symposium 2015, September 28  30, 2015, Burgstädt, September 29, 2015.

CH. Heinemann, Solvability of differential inclusions describing damage processes and applications to optimal control problems, Universität EssenDuisburg, Fakultät für Mathematik, Essen, December 3, 2015.

D. Peschka, Mathematical modeling, analysis, and optimization of strained germaniummicrobridges, sc Matheon Center Days, April 20  21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

J. Sprekels, Optimal boundary control problems for CahnHilliard systems with dynamic boundary conditions, INdAM Workshop ``Special Materials in Complex Systems  SMaCS 2015'', May 18  22, 2015, Rome, Italy, May 21, 2015.

M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an AllenCahn equation with dynamic boundary conditions, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 20, 2015.

M.H. Farshbaf Shaker, Introduction into optimal control of partial differential equations, May 14  18, 2015, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of).

M.H. Farshbaf Shaker, Multimaterial phase field approach to structural topology optimization and its relation to sharp interface approach, University of Tokyo, Graduate School of Mathematical Sciences, Japan, October 6, 2015.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 13, 2015.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, Technische Universität Berlin, Institut für Mathematik, February 5, 2015.

CH. Heinemann, Wellposedness of strong solutions for a damage model in 2D, Universitá di Brescia, Department DICATAM  Section of Mathematics, Italy, March 13, 2015.

R. Henrion, (Sub) Gradient formulae for probability functions with Gaussian distribution, PGMO Days 2015  Gaspard Monge Program for Optimization and Operations Research, October 27  28, 2015, ENSTA ParisTech, Palaiseau, France, October 28, 2015.

R. Henrion, (Sub)Gradient formulae for probability functions with applications to power management, Universidad de Chile, Centro de Modelamiento Matemático, Santiago de Chile, Chile, November 25, 2015.

R. Henrion, Calmness as a constraint qualification for MPECs, International Conference on Variational Analysis, Optimization and Quantitative Finance in Honor of Terry Rockafellar's 80th Birthday, May 18  22, 2015, Université de Limoges, France, May 21, 2015.

R. Henrion, Conditioning of linearquadratic twostage stochastic optimization problems, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic, March 26, 2015.

R. Henrion, On some relations between probability functions and variational analysis, International Workshop ``Variational Analysis and Applications'', August 28  September 5, 2015, Erice, Italy, August 31, 2015.

D. Hömberg, A crash course on optimal control, Fudan University, School of Mathematical Sciences, Shanghai, China, March 18, 2015.

D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems  SMaCS 2015'', May 18  22, 2015, Rome, Italy, May 21, 2015.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

D. Hömberg, The digital factory  A perspective for a closer cooperation between math and industry, Workshop ``Mathematics and Computer Science in Practice: Potential and Reality'', December 9  11, 2015, Prague, Czech Republic, December 9, 2015.

J. Sprekels, Optimal boundary control problems for CahnHilliard systems with singular potentials and dynamic boundary conditions, Romanian Academy, Simeon Stoilow Institute of Mathematics, Bucharest, March 18, 2015.

N. Togobytska, Optimal control approach for production of multiphase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hotrolling, June 9  13, 2014, Taormina, Italy, June 9, 2014.

M. Eigel, Guaranteed a posteriori error control with adaptive stochastic Galerkin FEM, SIAM Conference on Uncertainty Quantification (UQ14), March 31  April 3, 2014, Savannah, USA, April 1, 2014.

TH. Petzold, Modellierung, Simulation und Optimierung in angewandter Mathematik am WeierstraßInstitut, Innovation Days 2014, December 1  2, 2014, München, December 2, 2014.

K. Sturm, Optimal control and shape design problems in thermomechanics, BMSWIAS Summer School ``Applied Analysis for Materials'', August 25  September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 2, 2014.

M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an AllenCahn equation with dynamic boundary conditions and double obstacles, Conference on Partial Differential Equations, May 28  31, 2014, Novacella, Italy, May 29, 2014.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, SADCOWIAS Young Researcher Workshop, January 29  31, 2014, WIAS, January 31, 2014.

R. Henrion, Calmness as a constraint qualification for MPECs, German Polish Conference on Optimization Methods and Applications, February 28  March 4, 2014, Wittenberg, March 1, 2014.

R. Henrion, Calmness as a constraint qualification for MPECs, 6th Seminar on Optimization and Variational Analysis, University of Elche, Spain, June 3, 2014.

R. Henrion, Conditioning of linearquadratic twostage stochastic optimization problems, 5th Conference on Optimization Theory and its Applications (ALEL 2014), June 5  7, 2014, Universidad de Sevilla, Spain, June 6, 2014.

R. Henrion, Nichtlineare Optimierung bei unsicheren Nebenbedingungen, 1. Arbeitstreffen zur Initiative ``Biokybernetik'', November 20  21, 2014, Großkarlbach, November 20, 2014.

D. Hömberg, Modelling and simulation of multifrequency induction hardening, Ecole Polytechnique, Laboratoire de Mécanique des Solides, Palaiseau, France, March 13, 2014.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, October 21, 2014.

D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

D. Hömberg, Multifrequency induction hardening  Modelling, analysis, and simulation, Fudan University, School of Mathematical Sciences, Shanghai, China, March 4, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25  28, 2014, University of Warwick, UK, March 26, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hotrolling, June 9  13, 2014, Taormina, Italy, June 9, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

D. Hömberg, Optimal control and shape design problems in thermomechanics, BMSWIAS Summer School ``Applied Analysis for Materials'', August 25  September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

J. Sprekels, Introduction into the optimal control of PDEs, SADCOWIAS Young Researcher Workshop, January 29  31, 2014, WIAS, January 31, 2014.

CH. Landry, Collision detection between robots moving along specified paths, Universität der Bundeswehr München, Institut für Mathematik und Rechneranwendung, Neubiberg, May 15, 2013.

CH. Landry, Optimizing work cells in automotive industry, Mathematics for Industry and Society, July 4  5, 2013, French Embassy, Berlin, July 5, 2013.

CH. Landry, Task assignment, sequencing and pathplanning in robotic welding cells, 18th International Conference on Methods and Models in Automation and Robotics, August 26  29, 2013, Miedzyzdroje, Poland, August 27, 2013.

M. Eigel, Advances in adaptive stochastic Galerkin FEM, Workshop ``Partial Differential Equations with Random Coefficients'', November 13  15, 2013, WIAS, Berlin, November 14, 2013.

M. Eigel, On tensor approximations with adaptive stochastic Galerkin FEM, Eidgenössische Technische Hochschule Zürich, Seminar für Angewandte Mathematik, Switzerland, September 25, 2013.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, The Fourth International Conference on Continuous Optimization (ICCOPT), July 27  August 1, 2013, Universidade Nova de Lisboa, Lisbon, Portugal, July 31, 2013.

R. Henrion, Dual stationarity conditions for MPECs, CIMPAUNESCOMESRMINECOINDIA Research School ``Generalized Nash Equilibrium Problems, Bilevel Programming and MPES'', November 25  December 6, 2013, University of Delhi, India.

R. Henrion, Optimierungsprobleme mit Wahrscheinlichkeitsrestriktionen, Technische Universität Darmstadt, Fachbereich Mathematik, September 16, 2013.

R. Henrion, Optimization problems with probabilistic constraints, Workshop ``Numerical Methods for PDE Constrained Optimization with Uncertain Data'', January 27  February 2, 2013, Mathematisches Forschungsinstitut Oberwolfach, January 30, 2013.

R. Henrion, Optimization problems with probabilistic constraints, Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 8, 2013.

R. Henrion, Optimization problems with probabilistic constraints, March 19  21, 2013, University of Ostrava, Department of Mathematics, Czech Republic.

R. Henrion, Problèmes d'optimisation avec des contraintes en probabilité, Electricité de France, Clamart, France, June 20, 2013.

R. Henrion, Stochastic optimization with probabilistic constraints, International Conference on Stochastic Programming (SP XIII), July 8  12, 2013, Bergamo, Italy, July 9, 2013.

R. Henrion, Optimisation sous contraintes en probabilité, Journées annuelles 2013 du Groupe de Recherche MOA, June 17  19, 2013, Paris, France, June 17, 2013.

D. Hömberg, An optimal shape design approach towards distortion compensation, Equadiff13, MS21  Recent Trends in PDEconstrained Control and Shape Design, August 26  30, 2013, Prague, Czech Republic, August 29, 2013.

D. Hömberg, An optimal shape design approach towards distortion compensation, Fudan University, School of Mathematics, Shanghai, China, March 6, 2013.

D. Hömberg, Mathematics for the digital factory, Mathematics for Industry and Society, July 4  5, 2013, French Embassy, Berlin, July 5, 2013.

D. Hömberg, MeFreSim  Modellierung, Simulation und Optimierung des Mehrfrequenzverfahrens für die induktive Wärmebehandlung als Bestandteil der modernen Fertigung, BMBF Status Seminar ``Mathematik für Innovationen in Industrie und Dienstleistung'', June 20  21, 2013, Bonn, June 21, 2013.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Forum MathforIndustry 2013 ``The Impact of Applications on Mathematics'', November 4  8, 2013, Kyushu University, Fukuoka, Japan, November 7, 2013.

D. Hömberg, On a phase field approach to shape optimization, Université de ParisSud, Laboratoire de Mathématiques, Equipe Analyse Numérique et EDP, France, January 16, 2013.

D. Hömberg, Sufficient optimality conditions for a semilinear parabolic system, University of Tokyo, Graduate School of Mathematical Sciences, Japan, February 27, 2013.

J. Sprekels, Optimal control of AllenCahn equations with singular potentials and dynamic boundary conditions, DIMO2013  Diffuse Interface Models, September 10  13, 2013, Levico Terme, Italy, September 11, 2013.

J. Sprekels, Optimal control of the AllenCahn equation with dynamic boundary condition and double obstacle potentials: A ``deep quench'' approach, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 17, 2013.

CH. Landry, An optimal control problem for the collisionfree motion planning of industrial robots, École Polytechnique Fédérale de Lausanne, Mathematics Institute of Computational Science and Engineering (MATHICSE), Switzerland, November 28, 2012.

CH. Landry, Collisionfree path planning of welding robots, The 17th European Conference on Mathematics for Industry 2012 (ECMI 2012), July 23  27, 2012, Lund, Sweden, July 24, 2012.

CH. Landry, Modeling of the optimal trajectory of industrial robots in the presence of obstacles, 21st International Symposium on Mathematical Programming (ISMP), August 19  24, 2012, Technische Universität Berlin, August 22, 2012.

K. Sturm, Shape optimization for an interface problem in linear elasticity for distortion compensation, 21st International Symposium on Mathematical Programming (ISMP), August 19  24, 2012, Technische Universität Berlin, August 20, 2012.

R. Henrion, On (co)derivatives of the solution map to a class of generalized equations, 21st International Symposium on Mathematical Programming (ISMP), August 19  24, 2012, Technische Universität Berlin, August 23, 2012.

R. Henrion, On the coderivative of normal cone mappings to moving sets, 58th Course ``Variational Analysis and Applications'', May 14  22, 2012, International School of Mathematics ``Guido Stampacchia'', Erice, Italy, May 18, 2012.

D. Hömberg, On a phase field approach to topology optimization, MiniWorkshop ``Geometries, Shapes and Topologies in PDEbased Applications'', November 25  December 1, 2012, Mathematisches Forschungsinstitut Oberwolfach, November 27, 2012.

D. Hömberg, On the phase field approach to shape and topology optimization, University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 6, 2012.

D. Hömberg, Optimal control of multifrequency induction hardening, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17  21, 2012, Cortona, Italy, September 18, 2012.

D. Hömberg, Optimal control of multiphase steel production, 21st International Symposium on Mathematical Programming (ISMP), August 19  24, 2012, Technische Universität Berlin, August 23, 2012.

J. Sprekels, A time discretization for a nonstandard viscous CahnHilliard system, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17  21, 2012, Cortona, Italy, September 19, 2012.

J. Sprekels, Optimal control problems arising in the industrial growth of bulk semiconductor single crystals, 21st International Symposium on Mathematical Programming (ISMP), Invited Session ``Optimization Applications in Industry I'', August 19  24, 2012, Technische Universität Berlin, August 21, 2012.

J. Sprekels, Optimal control problems arising in the industrial growth of bulk single semiconductor crystals, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 11, 2012.

CH. Landry, A minimum time control problem for finding robot motion planning, Optimization 2011, July 24  27, 2011, Lisbon, Portugal, July 25, 2011.

TH. Arnold, On Born approximation for the scattering by rough surfaces, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 15, 2011.

A. Möller, Capacity planning in energy networks by probabilistic programming, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 14, 2011.

R. Henrion, Progress and challenges in chanceconstrained programming, SIGOPT  International Conference on Optimization 2011, June 15  17, 2011, PfalzAkademie Lambrecht, June 15, 2011.

D. Hömberg, Mathematical concepts in steel manufacturing, Fudan University, School of Mathematics, Shanghai, China, March 29, 2011.

D. Hömberg, Optimal boundary coefficient control for parabolic equations, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20  23, 2011, Gargnano (Brescia), Italy, June 20, 2011.

D. Hömberg, Optimal control problems in thermomechanics, Schwerpunktskolloquium ``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, January 20, 2011.

D. Hömberg, Solidsolid phase transitions: From surface hardening of steel to laser thermotherapy, Southeast University, Department of Mathematics, Nanjing, China, March 28, 2011.

J. Sprekels, A nonstandard phasefield system of CahnHilliard type for diffusive phase segregation, Schwerpunktkolloquium``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, July 14, 2011.

J. Sprekels, A nonstandard phase field system of CahnHilliard type for diffusive phase segregation, Seminario Matematico e Fisico di Milano, Università degli Studi di Milano, Dipartimento di Matematica, Italy, September 21, 2011.

R. Henrion, On calmness conditions in convex bilevel programming, SIAM Conference on Optimization, May 16  19, 2011, Darmstadt, May 16, 2011.

R. Henrion, On joint linear probabilistic constraints with Gaussian coefficient matrix, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 14, 2011.

R. Henrion, Structure, stability and algorithmic issues of optimization problems with probabilistic constraints, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 16, 2011.

D. Hömberg, Modelling, simulation and control of multiphase steel production, International Congress on Modelling and Simulation (MODSIM 2011), December 12  16, 2011, Perth, Australia, December 15, 2011.

D. Hömberg, On the phase field approach to shape and topology optimization, Università degli Studi di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, November 15, 2011.

K. Krumbiegel, Optimal control approach for production of modern multiphase steels, International Congress on Industrial and Applied Mathematics (ICIAM), July 18  22, 2011, Vancouver, Canada, July 18, 2011.

K. Krumbiegel, Superconvergence properties for semilinear elliptic boundary control problems, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 15, 2011.

J. Sprekels, Wellposedness, asymptotic behavior and optimal control of a nonstandard phase field model for diffusive phase segregation, Workshop on Optimal Control of Partial Differential Equations, November 28  December 1, 2011, Wasserschloss Klaffenbach, Chemnitz, November 30, 2011.

N. Togobytska, An inverse problem for laserinduced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23  24, 2010, September 24, 2010.

R. Henrion, Chanceconstrained problems, PreConference PhD Workshop, 12th Conference on Stochastic Programming (SPXII), Halifax, Canada, August 15, 2010.

R. Henrion, On a dynamic model for chance constrained programming, 12th Conference on Stochastic Programming (SPXII), August 16  20, 2010, Halifax, Canada, August 17, 2010.

R. Henrion, Optimization problems with probabilistic constraints, 3rd International Conference on Continuous Optimization (ICCOPT), July 26  29, 2010, Santiago de Chile, July 27, 2010.

D. Hömberg, A brief introduction to PDEconstrained control, Warsaw Seminar on Industrial Mathematics (WSIM'10), March 18  19, 2010, Warsaw University of Technology, Poland, March 18, 2010.

D. Hömberg, Steel manufacturing  A challenge for applied mathematics, Universität DuisburgEssen, Fachbereich Mathematik, May 11, 2010.

D. Hömberg, The mathematics of distortion, ``Seminario Matematico e Fisico di Milano'', Università degli Studi di Milano, Dipartimento di Matematica, Italy, March 1, 2010.

K. Krumbiegel, Numerical analysis for elliptic Neumann boundary control problems with pointwise state and control constraints, Technische Universität Dresden, Institut für Numerische Mathematik, May 11, 2010.

K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, May 18, 2010.

K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Summer School ``Optimal Control of Partial Differential Equations'', July 12  17, 2010, Cortona, Italy, July 16, 2010.

K. Krumbiegel, Sufficient optimality conditions for the MoreauYosida type regularization concept applied to state constrained problems, Gemeinsame Jahrestagung Deutsche MathematikerVereinigung (DMV) und Gesellschaft für Didaktik der Mathematik (GDM), March 8  12, 2010, LudwigMaximiliansUniversität München, March 10, 2010.

K. Krumbiegel, Sufficient optimality conditions for the MoreauYosida type regularization concept applied to state constrained problems, 81th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2010), March 22  26, 2010, Universität Karlsruhe, March 25, 2010.

J. Sprekels, Introduction to Optimal Control Problems for PDEs (minicourse), Summer School ``Optimal Control of Partial Differential Equations'', July 12  17, 2010, Cortona, Italy.

R. Henrion, A model for dynamic chance constraints in water reservoir management, 23rd European Conference on Operational Research (EURO23), July 6  8, 2009, Bonn, July 7, 2009.

R. Henrion, Answers and questions in selected topics of probabilistic programming, International Colloquium on Stochastic Modeling and Optimization, November 30  December 1, 2009, Rutgers University, New Brunswick, USA, November 30, 2009.

R. Henrion, On stationarity conditions for an equilibrium problem with equilibrium constraints from an electricity spot market model, 23rd European Conference on Operational Research (EURO23), July 6  8, 2009, Bonn, July 7, 2009.

D. Hömberg, Die Wärmebehandlung von Stahl  Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multiphase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9  11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

D. Hömberg, Distortion compensation  An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27  31, 2009, Buenos Aires, Argentina, July 27, 2009.

D. Hömberg, Optimal control of heat treatments and stability of milling processes  Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

K. Krumbiegel, Optimalsteuerung mit Zustandsbeschränkungen, Universität Leipzig, Fakultät für Mathematik und Informatik, October 6, 2009.

W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26  28, 2008.

R. Henrion, Distance to uncontrollability for convex processes, SIGOPT International Conference on Optimization, February 18  21, 2008, Lambrecht, February 19, 2008.

R. Henrion, On a dynamical model for chance constrained programming, Conference on Optimization & Practices in Industry (COPI08), November 26  28, 2008, Clamart, France, November 28, 2008.

R. Henrion, On calculating the normal cone to a finite union of convex polyhedra, World Congress of Nonlinear Analysts (WCNA 2008), July 2  9, 2008, Orlando, USA, July 3, 2008.

D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

D. Hömberg, Solidsolid phase transitions  Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

D. Hömberg, The heat treatment of steel  A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17  19, 2008, Bremen, September 19, 2008.

R. Henrion, Avoidance of random obstacles by means of probabilistic constraints, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16  20, 2007, ETH Zürich, Switzerland, July 16, 2007.

R. Henrion, Chanceconstrained stochastic programming, Spring School on Stochastic Programming: Theory and Applications, University of Bergamo, Italy, April 12, 2007.

R. Henrion, Contraintes en probabilité: synthèse bibliographique et approche à la situation dynamique, Electricité de France R&D, Clamart, France, November 28, 2007.

R. Henrion, Distance to uncontrollability for convex processes, International Congress ``Mathematical Methods in Economics and Industry'' (MMEI 2007), June 37, Herlany, Slovakia, June 5, 2007.

R. Henrion, Eventual convexity and related properties of probabilistic constraints, 11th Conference on Stochastic Programming (SPXI), August 27  31, 2007, Vienna, Austria, August 31, 2007.

D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16  20, 2007, ETH Zürich, Switzerland, July 19, 2007.

D. Hömberg, A short course on PDEconstrained optimal control, March 20  30, 2007, Universitá degli Studi di Milano, Dipartimento di Matematica, Italy.

D. Hömberg, Mathematical tools for the simulation and control of heat treatments, Delphi, Puerto Real, Spain, January 16, 2007.

D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part I), University of Tokyo, Department of Mathematical Sciences, Japan, February 21, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part II), University of Tokyo, Department of Mathematical Sciences, Japan, February 22, 2007.

D. Hömberg, Thermomechanical phase transition models  analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

R. Henrion, Initiation aux contraintes en probabilité, Electricité de France R&D, Clamart, France, May 17, 2006.

R. Henrion, On chance constraints with random coefficient matrix, 19th International Symposium on Mathematical Programming (ISMP 2006), Rio de Janeiro, Brazil, August 3, 2006.

R. Henrion, Quelques propriétés structurelles de contraintes en probabilité, Ecole Nationale des Ponts et Chaussées, MarnelaVallée, France, May 16, 2006.

R. Henrion, Structural analysis for some basic types of probabilistic constraints, Prague Stochastics 2006, Czech Republic, August 25, 2006.

D. Hömberg, A crash course in Nonlinear Optimization, November 13  23, 2006, Escuela Politécnica Nacional, Quito, Ecuador.

D. Hömberg, Die Wärmebehandlung von Stahl  ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

D. Hömberg, Laser surface hardening  modelling, simulation and optimal control, 4th KoreanGerman Seminar on Applied Mathematics and Physics, September 24  October 1, 2006, Erlangen, September 26, 2006.

D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28  31, 2006, Miedzyzdroje, Poland, August 29, 2006.

D. Hömberg, Optimal control of laser material treatments, 21st European Conference on Operational Research (EURO XXI), July 3  5, 2006, Reykjavik, Iceland, July 3, 2006.

D. Hömberg, Optimal control of thermomechanical phase transitions, Workshop ``Inverse and Control Problems for PDE's'', March 13  17, 2006, Rome, Italy, March 13, 2006.

D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14  18, 2006, Föhr.

D. Hömberg, Thermomechanical models of phase transitions  modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

R. Henrion, T. Szántai, Properties and calculation of singular normal distributions, Dagstuhl Seminar on ``Algorithms for Optimization with Incomplete Information'', Schloss Dagstuhl, January 17, 2005.

R. Henrion, Calmness of chance constraints and Lipschitz properties of the valueatrisk, 22nd IFIP TC 7 Conference on System Modeling and Optimization, July 18  22, 2005, Turin, Italy, July 21, 2005.

R. Henrion, On the structure of linear chance constraints with random coefficients, Conference on Optimization under Uncertainties (COUCH 2005), September 28  30, 2005, Heidelberg, September 29, 2005.

R. Henrion, Properties of linear probabilistic constraints, INFORMS Annual Meeting, November 13  16, 2005, San Francisco, USA, November 14, 2005.

R. Henrion, Stability of solutions in programs with probabilistic constraints, 10th Workshop on Wellposedness of Optimization Problems and Related Topics, September 5  9, 2005, Borovets, Bulgaria, September 9, 2005.

D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7  12, 2005, Coimbra, Portugal, June 11, 2005.

D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24  26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

D. Hömberg, Die Laserhärtung von Stahl  Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

D. Hömberg, Laser material treatments  modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25  29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

D. Hömberg, Optimal control of solidsolid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17  23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie  Simulations und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3  4, 2005, Frankfurt am Main, November 3, 2005.

R. Henrion, J. Outrata, Calmness of constraint systems with applications, FrenchGermanSpanish Conference on Optimization, September 20  24, 2004, University of Avignon, France, September 21, 2004.

R. Henrion, (Sub)Differentiability and Lipschitz properties of singular normal distributions, 10th International Conference on Stochastic Programming, October 8  15, 2004, University of Arizona, Tucson, USA, October 15, 2004.

R. Henrion, Optimization problems with probabilistic constraints, 10th International Conference on Stochastic Programming, October 8  15, 2004, University of Arizona, Tucson, USA, October 9, 2004.

R. Henrion, Selected aspects of structure, stability and numerics in chanceconstrained optimization problems, Workshop on Optimization of Stochastic Systems, Stevens Institute of Technology, Hoboken, USA, April 30, 2004.

R. Henrion, Some results on stability, structure and numerics in programs with probabilistic constraints, Universität Zürich, Wirtschaftswissenschaftliche Fakultät, Switzerland, December 20, 2004.

R. Henrion, Sur des applications multivôques du type 'calme', Séminaire de l'Equipe ACSIOM (Analyse, Calcul Scientifique Industriel et Optimisation de Montpellier), Université Montpellier, France, November 16, 2004.

D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

D. Hömberg, The induction hardening of steel  Modelling, analysis and optimal design of inductor coils, University of Kyoto, Department of Mathematics, Japan, October 21, 2004.

D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl  Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

O. Klein, Optimierung des Temperaturfeldes bei der Sublimationszüchtung von SiC Einkristallen, DGKK Arbeitskreis Angewandte Simulation in der Kristallzüchtung, February 5  6, 2004, Deutsche Gesellschaft für Kristallwachstum und Kristallzüchtung e.V., Volkach, February 5, 2004.

C. Meyer, O. Klein, P. Philip, A. Rösch, J. Sprekels, F. Tröltzsch, Optimal"steuerung bei der Herstellung von SiCEinkristallen, MathInsideÜberall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003.

R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, 18th International Symposium on Mathematical Programming (ISMP 2003), August 18  22, 2003, Copenhagen, Denmark, August 18, 2003.

R. Henrion, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Charles University, Institute of Mathematics, Prague, Czech Republic, April 24, 2003.

D. Hömberg, Optimal design of inductor coils, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7  11, 2003, Sydney, Australia, July 10, 2003.

D. Hömberg, Surface hardening of steel  Part I: Optimal design of inductor coils, 9th IEEE International Conference on Methods and Models in Automation and Robotics, August 25  28, 2003, Miedzyzdroje, Poland, August 26, 2003.
Preprints im Fremdverlag

A. Ivanova, P. Dvurechensky, A. Gasnikov, Composite optimization for the resource allocation problem, Preprint no. arXiv:1810.00595, Cornell University Library, arXiv.org, 2018.
Abstract
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium. 
Y. Nesterov, A. Gasnikov, S. Guminov, P. Dvurechensky, Primaldual accelerated gradient descent with line search for convex and nonconvex optimization problems, Preprint no. arXiv:1809.05895, Cornell University Library, arXiv.org, 2018.
Abstract
In this paper a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the wellknown lower bounds for both convex and nonconvex objective functions, possesses primaldual properties and can be applied in the noneuclidian setup. As far as we know this is the first such method possessing all of the above properties at the same time. We demonstrate how in practice one can efficiently use the combination of linesearch and primalduality by considering a convex optimization problem with a simple structure (for example, affinely constrained). 
P. Dvurechensky, A. Gasnikov, A. Kroshnin, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, Preprint no. arXiv:1802.04367, Cornell University Library, arXiv.org, 2018.

P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primaldual method for searching equilibrium in hierarchical congestion population games, Preprint no. arXiv:1606.08988, Cornell University Library, arXiv.org, 2016.
Abstract
In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multilevel convex optimization problem. We propose a fast primaldual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity. 
R. Hildebrand, Spectrahedral cones generated by rank 1 matrices, Preprint no. arXiv:1409.4781, Cornell University Library, arXiv.org, 2014.

P.J.C. Dickinson, R. Hildebrand, Considering copositivity locally, Preprint no. 4315, Optimization Online, optimizationonline.org, 2014.
Abstract
Let A be an element of the copositive cone COPn. A zero u of A is a nonnegative vector whose elements sum up to one and such that uTAu = 0. The support of u is the index set supp u f1; : : : ; ng corresponding to the nonzero entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u. Our main result is a characterization of the cone of feasible directions at A, i.e., the convex cone KA of real symmetric nn matrices B such that there exists > 0 satisfying A + B 2 COPn. This cone is described by a set of linear inequalities on the elements of B constructed from the set of zeros of A and their supports. This characterization furnishes descriptions of the minimal face of A in COPn, and of the minimal exposed face of A in COPn, by sets of linear equalities and inequalities constructed from the set of minimal zeros of A and their supports. In particular, we can check whether A lies on an extreme ray of COPn by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sucient condition on the irreducibility of A with respect to a copositive matrix C. Here A is called irreducible with respect to C if for all > 0 we have A ?? C 62 COPn.
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