Mathematical Topic "Optimal control of partial differential equations and nonlinear optimization"

D. Hömberg, F. Tröltzsch, eds., System Modeling and Optimization, 25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 2011, 391 of IFIP AICT, Springer, --- Heidelberg, 2013, 568 pages, (conference 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, (conference 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. 279--299, (chapter published).

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

P. Colli, G. Gilardi, P. Podio-Guidugli, J. Sprekels, An asymptotic analysis for a nonstandard Cahn--Hilliard system with viscosity, Discrete Contin. Dyn. Syst. Ser. S, 6 (2013) pp. 353--368.
Abstract

This paper is concerned with a diffusion model of phase-field 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 well-posed and investigated the long-time 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 long-time 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 J. Control Optim., 51 (2013) pp. 301--331.
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.

D. Hömberg, K. Krumbiegel, J. Rehberg, Boundary coefficient control --- A maximal parabolic regularity approach, Appl. Math. Optim., 67 (2013) pp. 3--31.
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. Podio-Guidugli, J. Sprekels, Distributed optimal control of a nonstandard system of phase field equations, Contin. Mech. Thermodyn., 24 (2012) pp. 437--459.
Abstract

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species 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 first-order necessary conditions of optimality.

P. Colli, G. Gilardi, J. Sprekels, Analysis and optimal boundary control of a nonstandard system of phase field equations, Milan J. Math., 80 (2012) pp. 119--149.
Abstract

We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in Podio-Guidugli (2006), describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in Colli, Gilardi, Podio-Guidugli, 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 well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order 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, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 19 (2012) pp. 117--159.

M. Gerdts, R. Henrion, D. Hömberg, Ch. Landry, Path planning and collision avoidance for robots, Numer. Algebra Control Optim., 2 (2012) pp. 437--463.
Abstract

An optimal control problem to find the fastest collision-free 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 M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market, ESAIM Control Optim. Calc. Var., 18 (2012) pp. 295--317.
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, so-called $M$-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 co-derivative 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 two-settlements 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 J. Math., 80 (2012) pp. 311--332.
Abstract

This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called 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 initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life 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 non-unique multiplier, Math. Program., 136 (2012) pp. 111--131.

K. Krumbiegel, I. Neitzel, A. Rösch, Regularization error estimates for semilinear elliptic optimal control problems with pointwise state and control constraints, Comput. Optim. Appl., 52 (2012) pp. 181--207.
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 three-dimensional state-constrained induction heating problems with nonlocal radiation effects, SIAM J. Control Optim., 49 (2011) pp. 1707--1736.
Abstract

The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic 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 temperature-dependent 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 control-to-state 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, Appl. Anal., 90 (2011) pp. 951--970.
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 so-called 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, Internat. Ser. Oper. Res. Management Sci., 163 (2011) pp. 427--439.

J. Sprekels, D. Tiba, Extensions of the control variational method, Control Cybernet., 40 (2011) pp. 1099--1108.
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 time-dependent problems.

A. Caboussat, Ch. Landry, J. Rappaz, Optimization problem coupled with differential equations: A numerical algorithm mixing an interior-point method and event detection, J. Optim. Theory Appl., 147 (2010) pp. 141--156.

M.J. Fabian, R. Henrion, A.Y. Kruger, J. Outrata, Error bounds: Necessary and sufficient conditions, Set-Valued Var. Anal., 18 (2010) pp. 121--149.
Abstract

The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

R. Henrion, B. Mordukhovich, N.M. Nam, Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM J. Optim., 20 (2010) pp. 2199--2227.

R. Henrion, J. Outrata, Th. Surowiec, A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints, Kybernetika, 46 (2010) pp. 423--434.
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 multiplier-based stationarity condition can be derived. This is applied then to an equilibrium model arising from ISO-regulated electricity spot markets.

R. Henrion, W. Römisch, Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions, Ann. Oper. Res., 177 (2010) pp. 115--125.

R. Henrion, A. Seeger, Inradius and circumradius of various convex cones arising in applications, Set-Valued Var. Anal., 18 (2010) pp. 483--511.

R. Henrion, A. Seeger, On properties of different notions of centers for convex cones, Set-Valued Var. Anal., 18 (2010) pp. 205--231.

D. Hömberg, Ch. Meyer, J. Rehberg, W. Ring, Optimal control for the thermistor problem, SIAM J. Control Optim., 48 (2010) pp. 3449--3481.
Abstract

This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear 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 first-order 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 J. Control Optim., 48 (2010) pp. 5108--5142.

K. Krumbiegel, I. Neitzel, A. Rösch, Sufficient optimality conditions for the Moreau--Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints, Ann. Acad. Rom. Sci. Math. Appl., 2 (2010) pp. 222--246.
Abstract

We develop sufficient optimality conditions for a Moreau-Yosida 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 Moreau-Yosida 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, Ch. Küchler, W. Römisch, Scenario reduction in stochastic programming with respect to discrepancy distances, Comput. Optim. Appl., 43 (2009) pp. 67--93.

R. Henrion, J. Outrata, Th. Surowiec, On the co-derivative of normal cone mappings to inequality systems, Nonlinear Anal., 71 (2009) pp. 1213--1226.
Abstract

The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both, the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz 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, Materialwiss. Werkstofftech., 40 (2009) pp. 438--442.
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 machine-based control.

D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Appl. Anal., 88 (2009) pp. 669--681.
Abstract

The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solid-solid 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, Comput. Optim. Appl., 43 (2009) pp. 213--233.

J. Sprekels, D. Tiba, The control variational approach for differential systems, SIAM J. Control Optim., 47 (2009) pp. 3220--3236.

P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Res. Int., 79 (2008) pp. 793--799.
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 two-stage stochastic integer programming, J. Indust. Management Optim., 4 (2008) pp. 363--384.

R. Henrion, J. Outrata, On calculating the normal cone to a finite union of convex polyhedra, Optimization, 57 (2008) pp. 57--78.

R. Henrion, A. Seeger, Uniform boundedness of norms of convex and nonconvex processes, Numer. Funct. Anal. Optim., 29 (2008) pp. 551--573.

R. Henrion, C. Strugarek, Convexity of chance constraints with independent random variables, Comput. Optim. Appl., 41 (2008) pp. 263--276.

D. Dentcheva, R. Henrion, A. Ruszczynski, Stability and sensitivity of optimization problems with first order stochastic dominance constraints, SIAM J. Optim., 18 (2007) pp. 322--337.

C. Lefter, J. Sprekels, Optimal boundary control of a phase field system modeling nonisothermal phase transitions, Adv. Math. Sci. Appl., 17 (2007) pp. 181-194.

R. Henrion, W. Römisch, On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling, Appl. Math., 522 (2007) pp. 473--494.
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) multi-leader-follower 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 co-derivative of the normal cone mapping to a polyhedron is derived (Proposition 3.2). Later the co-derivative formula is used for verifying constraint qualifications and for identifying M-stationary 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, 56 (2007) pp. 425--440.

R. Henrion, A. Lewis, A. Seeger, Distance to uncontrollability for convex processes, SIAM J. Optim., 45 (2006) pp. 26--50.

R. Henrion, Some remarks on value-at-risk optimization, Int. J. Management Sci. Engrg. Management, 1 (2006) pp. 111--118.

V. Arnăutu, J. Sprekels, D. Tiba, Optimization problems for curved mechanical structures, SIAM J. Control Optim., 44 (2005) pp. 743--775.

R. Henrion, J. Outrata, Calmness of constraint systems with applications, Math. Program., 104 (2005) pp. 437--464.

P. Bosch, A. Jourani, R. Henrion, Sufficient conditions for error bounds and applications, Appl. Math. Optim., 50 (2004) pp. 161--181.

R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Math. Program., 100 (2004) pp. 589--611.

R. Henrion, A. Möller, Optimization of a continuous distillation process under random inflow rate, Comput. Math. Appl., 45 (2003) pp. 247--262.

D. Hömberg, J. Sokolowski, Optimal shape design of inductor coils for induction hardening, SIAM J. Control Optim., 42 (2003) pp. 1087--1117.

D. Hömberg, S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition, Math. Comput. Modelling, 38 (2003) pp. 1003-1028.

J. Sprekels, D. Tiba, Optimization of clamped plates with discontinuous thickness, Systems Control Lett., 48 (2003) pp. 289-295.

A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches, SIAM J. Control Optim., 40 (2001) pp. 1107-1133.

V. Arnăutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates, Numer. Funct. Anal. Optim., 21 (2000) pp. 337--354.

J. Sprekels, D. Tiba, Sur les arches lipschitziennes, C. R. Math. Acad. Sci. Paris, 331 (2000) pp. 179--184.

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. 33--38.

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. 3334--3341.

D. Kern, Die Welt des Herrn Kuhn, in: Besser als Mathe --- Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. Lutz-Westphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 141--150.

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. 227--254.

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, 17--19 September 2008, Bremen, Germany, H.-W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201--209.

CH. Meyer, D. Hömberg, J. Rehberg, W. Ring, Optimal control of the thermistor problem, in: Optimal Control of Coupled Systems of PDE, Workshop, March 2--8, 2008, 5 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2008, pp. 624-626.

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. 39--55.

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. 259-271.

R. Henrion, Perturbation analysis of chance-constrained 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. 257--274.

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. 325--335.

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. 334--343.

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 10--14, 2002, Constanta, Romania, V. Barbu, I. Lasiecka, D. Tiba, C. Varsan, eds., Kluwer Academic Publishers, Boston, 2003, pp. 387--398.

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. 245-257.

M. Graf, D. Hömberg, R. Kawalla, N. Togobytska, W. Weiss, Identification, simulation and optimal control of heat transfer in cooling line of hot strip rolling mill, Preprint no. 1769, WIAS, Berlin, 2013.
Abstract

The numerical simulation of mechanical properties of hot-rolled products has a major significance for material characterisation as well as material development. The basis for these is the knowledge about the material-specific phase transformations in combination with the initial microstructure from the deformation steps before entering into the cooling line. Additionally, the technological conditions in the run-out table (ROT) are essentially for transformation kinetics. In order to simulate these processes, the plant-specific heat transfer coefficient must be measured. Therefore, steel samples with thermocouples inside are transported with defined velocities through the cooling line of the continuous pilot plant at the Institute of Metal Forming in Freiberg. Furthermore, the material and its movement must be taken into account as characteristics of the ROT (e.g. amount and distribution of the cooling medium, the streaming situation in several segments, the nozzle geometry and, as a consequence, the water jet shape, and the impact pressure of the cooling medium on the surface of the rolled material) as influencing parameters. This paper describes the possibilities for determining and simulating the heat transfer in the cooling line with industrial conditions. Moreover, this paper discusses the optimal control of the cooling line to achieve the desired temperature and phase distribution on the run-out table. The resulting information contributes to new technology and material developments at the pilot plant, as well as for the transfer of results into the industry.

P. Colli, J. Sprekels, Optimal control of an Allen--Cahn equation with singular potentials and dynamic boundary condition, Preprint no. 1750, WIAS, Berlin, 2012.
Abstract, PDF (212 kByte)

In this paper, we investigate optimal control problems for Allen--Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace--Beltrami 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 Laplace--Beltrami 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 well-posedness and regularity results for the state equation and then show the existence of optimal controls and that the control-to-state mapping is twice continuously Fréchet differentiable between appropriate function spaces. Based on these results, we establish the first-order necessary optimality conditions in terms of a variational inequality and the adjoint state equation, and we prove second-order sufficient optimality conditions.

P.-E. Druet, Some mathematical problems related to the 2nd order optimal shape of a crystallization interface, Preprint no. 1708, WIAS, Berlin, 2012.
Abstract, Postscript (464 kByte), PDF (241 kByte)

We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solid-liquid interface in a two-phase 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.

R. Henrion, J. Outrata, Th. Surowiec, On regular coderivatives in parametric equilibria with non-unique multipliers, Preprint no. 1686, WIAS, Berlin, 2012.
Abstract, Postscript (20 MByte), PDF (407 kByte)

This paper deals with the computation of regular coderivatives of solution maps associated with a frequently arising class of generalized equations. The constraint sets are given by (not necessarily convex) inequalities, and we do not assume linear independence of gradients to active constraints. The achieved results enable us to state several versions of sharp necessary optimality conditions in optimization problems with equilibria governed by such generalized equations. The advantages are illustrated by means of examples.

R. Henrion, A. Kruger, J. Outrata, Some remarks on stability of generalized equations, Preprint no. 1678, WIAS, Berlin, 2012.
Abstract, Postscript (4110 kByte), PDF (263 kByte)

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 multi-valued 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 Mangasarian-Fromovitz 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.

G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process, Preprint no. 1619, WIAS, Berlin, 2011.
Abstract, Postscript (1637 kByte), PDF (298 kByte)

We formulate and study an optimal control problem for the sweeping (Moreau) process, where control functions enter the moving sweeping set. To the best of our knowledge, this is the first study in the literature devoted to optimal control of the sweeping process. We first establish an existence theorem of optimal solutions and then derive necessary optimality conditions for this optimal control problem of a new type, where the dynamics is governed by discontinuous differential inclusions with variable right-hand sides. Our approach to necessary optimality conditions is based on the method of discrete approximations and advanced tools of variational analysis and generalized differentiation. The final results obtained are given in terms of the initial data of the controlled sweeping process and are illustrated by nontrivial examples.

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

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

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

CH. Landry, Collision-free 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, Mini-Workshop ``Geometries, Shapes and Topologies in PDE-based 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 Cahn--Hilliard 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 chance-constrained programming, SIGOPT --- International Conference on Optimization 2011, June 15 - 17, 2011, Pfalz-Akademie Lambrecht, June 15, 2011.

D. Hömberg, Mathematical concepts in steel manufacturing, Fudan University, School of Mathematics, Shanghai, Republic of 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, Solid-solid phase transitions: From surface hardening of steel to laser thermo-therapy, Southeast University, Department of Mathematics, Nanjing, Republic of China, March 28, 2011.

J. Sprekels, A non-standard phase-field system of Cahn--Hilliard 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 Cahn--Hilliard 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, Well-posedness, 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 laser-induced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23 - 24, 2010, September 24, 2010.

R. Henrion, Chance-constrained problems, Pre-Conference 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 PDE-constrained 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 Duisburg-Essen, 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 Moreau--Yosida type regularization concept applied to state constrained problems, Gemeinsame Jahrestagung Deutsche Mathematiker-Vereinigung (DMV) und Gesellschaft für Didaktik der Mathematik (GDM), March 8 - 12, 2010, Ludwig-Maximilians-Universität München, March 10, 2010.

K. Krumbiegel, Sufficient optimality conditions for the Moreau-Yosida 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 (mini-course), 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 multi-phase 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, Solid-solid 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, Chance-constrained 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 3--7, 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 PDE-constrained 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, Marne-la-Vallée, 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 Korean-German 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 value-at-risk, 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, 10-th Workshop on Well-posedness 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 solid-solid 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, French-German-Spanish 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 chance-constrained 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 SiC-Einkristallen, MathInside---Überall 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.