Nichtglatte Variationsprobleme und Operatorgleichungen

Publikationen

Monografien

• M. Hintermüller, R. Herzog, Ch. Kanzow, M. Ulbrich, S. Ulbrich, eds., Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, 172 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2022, viii + 519 pages, (Collection Published), DOI 10.1007/978-3-030-79393-7 .

Artikel in Referierten Journalen

• A. Alphonse, D. Caetano, A. Djurdjevac, Ch.M. Elliot, Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs, Journal of Differential Equations, 353 (2023), pp. 268-338, DOI 10.1016/j.jde.2022.12.032 .
  Abstract
  We develop a functional framework suitable for the treatment of partial differential equations and variational problems on evolving families of Banach spaces. We propose a definition for the weak time derivative that does not rely on the availability of a Hilbertian structure and explore conditions under which spaces of weakly differentiable functions (with values in an evolving Banach space) relate to classical Sobolev?Bochner spaces. An Aubin?Lions compactness result is proved. We analyse concrete examples of function spaces over time-evolving spatial domains and hypersurfaces for which we explicitly provide the definition of the time derivative and verify isomorphism properties with the aforementioned Sobolev?Bochner spaces. We conclude with the proof of well posedness for a class of nonlinear monotone problems on an abstract evolving space (generalising the evolutionary p-Laplace equation on a moving domain or surface) and identify some additional problems that can be formulated with the setting developed in this work.

• M. Hintermüller, A. Kröner, Differentiability properties for boundary control of fluid-structure interactions of linear elasticity with Navier--Stokes equations with mixed-boundary conditions in a channel, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 87 (2023), pp. 15/1--15/38, DOI 10.1007/s00245-022-09938-0 .
  Abstract
  In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generaziling the results of [Wollner and Wick, J. Math. Fluid Mech., 21, 2019] to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.

• M. Bongarti, I. Lasiecka, J.H. Rodrigues, Boundary stabilization of the linear MGT equation with partially absorbing boundary data and degenerate viscoelasticity, Discrete and Continuous Dynamical Systems -- Series S, 15 (2022), pp. 1355--1376, DOI 10.3934/dcdss.2022020 .

• M. Bongarti, I. Lasiecka, Boundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundary, Discrete and Continuous Dynamical Systems -- Series S, 15 (2022), pp. 1957--1985, DOI 10.3934/dcdss.2022107 .

• M. Bongarti, L.D. Galvan, L. Hatcher, M.R. Lindstrom, Ch. Parkinson, Ch. Wang, A.L. Bertozzi , Alternative SIAR models for infectious diseases and applications in the study of non-compliance, Mathematical Models & Methods in Applied Sciences, 32 (2022), pp. 1987--2015, DOI 10.1142/S0218202522500464 .
  Abstract
  In this paper, we use modified versions of the SIAR model for epidemics to propose two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of an infectious disease. The SIAR model distinguishes between symptomatic infected (I) and asymptomatic infected (A) populations. One modification, which is simpler, assumes a known proportion of the population does not comply with government mandates such as quarantining and social-distancing. In a more sophisticated approach, the modified model treats non-compliant behavior as a social contagion. We theoretically explore different scenarios such as the occurrence of multiple waves of infections. Local and asymptotic analyses for both models are also provided.

• J.C. De Los Reyes, K. Herrera, Parameter space study of optimal scale-dependent weights in TV image denoising, Applicable Analysis. An International Journal, published online on 03.02.2022, DOI 10.1080/00036811.2022.2033231 .

• M. Brokate, M. Ulbrich, Newton differentiability of convex functions in normed spaces and of a class of operators, SIAM Journal on Optimization, 32 (2022), pp. 1265--1287, DOI 10.1137/21M1449531 .

• G. Dong, M. Hintermüller, K. Papafitsoros, Optimization with learning-informed differential equation constraints and its applications, ESAIM. Control, Optimisation and Calculus of Variations, 28 (2022), pp. 3/1--3/44, DOI 10.1051/cocv/2021100 .
  Abstract
  Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned 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.

• C. Geiersbach, M. Hintermüller, Optimality conditions and Moreau--Yosida regularization for almost sure state constraints, ESAIM. Control, Optimisation and Calculus of Variations, 28 (2022), pp. 80/1--80/36, DOI 10.1051/cocv/2022070 .
  Abstract
  We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient optimality conditions for problems subject to equality and conical constraints. We propose a Moreau--Yosida regularization for the conical constraint and show consistency of the optimality conditions for the regularized problem as the regularization parameter is taken to infinity.

• A. Alphonse, C.N. Rautenberg, J.F. Rodrigues, Analysis of a quasi-variational contact problem arising in thermoelasticity, Nonlinear Analysis. An International Mathematical Journal, 217 (2022), pp. 112728/1--112728/40, DOI 10.1016/j.na.2021.112728 .
  Abstract
  We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling is determined by the thermal displacement of the mould that depends in turn on the membrane through the contact region. The two models considered are a stationary (or elliptic) model and an evolutionary (or quasistatic) one. For the first model, we prove the existence of weak solutions by solving an elliptic quasi-variational inequality coupled to elliptic equations. By exploring the fine properties of the variation of the contact set under non-degenerate data, we give sufficient conditions for the existence of regular solutions, and under certain contraction conditions, also a uniqueness result. We apply these results to a series of semi-discretised problems that arise as approximations of regular solutions for the evolutionary or quasistatic problem. Here, under certain conditions, we are able to prove existence for the evolutionary problem and for a special case, also the uniqueness of time-dependent solutions.

• A. Alphonse, M. Hintermüller, C.N. Rautenberg, On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities, Journal of Mathematical Analysis and Applications, 507 (2022), pp. 125732/1--125732/19, DOI 10.1016/j.jmaa.2021.125732 .
  Abstract
  In this short note, we prove that the minimal and maximal solution maps associated to elliptic quasi-variational 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 quasi-variational inequalities, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 30 (2022), pp. 873--922, DOI 10.1007/s11228-021-00624-x .
  Abstract
  We focus on elliptic quasi-variational 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.

• M. Hintermüller, K. Papafitsoros, C.N. Rautenberg, H. Sun, Dualization and automatic distributed parameter selection of total generalized variation via bilevel optimization, Numerical Functional Analysis and Optimization. An International Journal, 43 (2022), pp. 887--932, DOI 10.1080/01630563.2022.2069812 .
  Abstract
  Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order 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 statistics-based upper level objective is proposed in order to automatically select these parameters. The framework allows for spatially varying parameters, thus enabling better recovery in high-detail 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.

Beiträge zu Sammelwerken

• A. Alphonse, M. Hintermüller, C.N. Rautenberg, Stability and sensitivity analysis for quasi-variational inequalities, in: Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, M. Hintermüller, R. Herzog, Ch. Kanzow, M. Ulbrich, S. Ulbrich, eds., 172 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2022, pp. 183--210.

• J.C. De Los Reyes, D. Villacís, Bilevel optimization methods in imaging, in: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, K. Chen, C.-B. Schönlieb, X.-Ch. Tai, L. Younces, eds., published online on 17.02.2022, Springer, Cham, DOI 10.1007/978-3-030-03009-4_66-1 .

• D. Gahururu, M. Hintermüller, S.-M. Stengl, Th.M. Surowiec, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms and risk aversion, in: Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, M. Hintermüller, R. Herzog, Ch. Kanzow, M. Ulbrich, S. Ulbrich, eds., 172 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2022, pp. 145--181.

• C. Grässle, M. Hintermüller, M. Hinze, T. Keil, Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities, in: Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, M. Hintermüller, R. Herzog, Ch. Kanzow, M. Ulbrich, S. Ulbrich, eds., 172 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2022, pp. 211--240.

• S.H.K. Narayanan, Th. Propson, M. Bongarti, J. Hückelheim, P. Hovland, Reducing memory requirements of quantum optimal control, in: ICCS 2022: Computational Science -- ICCS 2022, D. Groen, C. DE Mulatier, M. Paszynski, V.V. Krzhizhanovskaya, J.J. Dongarra, P.M.A. Sloot, eds., 13353 of Lecture Notes in Computer Science, Springer, Cham, pp. published online on 15.06.2022, DOI 10.1007/978-3-031-08760-8_11 .

• C. Geiersbach, E. Loayza-Romero, K. Welker, PDE-Constrained Shape Optimization: Towards Product Shape Spaces and Stochastic Models, in: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, K. Chen, C.-B. Schönlieb, X.-Ch. Tai, L. Younces, eds., Springer, DOI 10.1007/978-3-030-03009-4_120-1 .
  Abstract
  Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which a so-called shape functional is constrained by a partial differential equation (PDE) describing the underlying physics. A connection can be made between a classical view of shape optimization and the differential geometric structure of shape spaces. To handle problems where a shape functional depends on multiple shapes, a theoretical framework is presented, whereby the optimization variable can be represented as a vector of shapes belonging to a product shape space. The multi-shape gradient and multi-shape derivative are defined, which allows for a rigorous justification of a steepest descent method with Armijo backtracking. As long as the shapes as subsets of a hold-all domain do not intersect, solving a single deformation equation is enough to provide descent directions with respect to each shape. Additionally, a framework for handling uncertainties arising from inputs or parameters in the PDE is presented. To handle potentially high-dimensional stochastic spaces, a stochastic gradient method is proposed. A model problem is constructed, demonstrating how uncertainty can be introduced into the problem and the objective can be transformed by use of the expectation. Finally, numerical experiments in the deterministic and stochastic case are devised, which demonstrate the effectiveness of the presented algorithms.

Preprints, Reports, Technical Reports

• A. Alphonse, D. Caetano, A. Djurdjevac, Ch.M. Elliott, Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs, Preprint no. 2994, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.2994 .
  Abstract, PDF (527 kByte)
  We develop a functional framework suitable for the treatment of partial differential equations and variational problems on evolving families of Banach spaces. We propose a definition for the weak time derivative that does not rely on the availability of a Hilbertian structure and explore conditions under which spaces of weakly differentiable functions (with values in an evolving Banach space) relate to classical Sobolev-Bochner spaces. An Aubin-Lions compactness result is proved. We analyse concrete examples of function spaces over time-evolving spatial domains and hypersurfaces for which we explicitly provide the definition of the time derivative and verify isomorphism properties with the aforementioned Sobolev-Bochner spaces. We conclude with the proof of well posedness for a class of nonlinear monotone problems on an abstract evolving space (generalising the evolutionary p-Laplace equation on a moving domain or surface) and identify some additional problems that can be formulated with the setting developed in this work.

• G. Dong, M. Hintermüller, K. Papafitsoros, A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives, Preprint no. 2964, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2964 .
  Abstract, PDF (748 kByte)
  We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and are approximated by nonsmooth ReLU neural networks. We first show that a direct smoothing of the ReLU network with the aim to make use of classical numerical solvers can have certain disadvantages, namely potentially introducing multiple solutions for the corresponding state equation. This motivates us to devise a numerical algorithm that treats directly the nonsmooth optimal control problem, by employing a descent algorithm inspired by a bundle-free method. Several numerical examples are provided and the efficiency of the algorithm is shown.

• A. Alphonse, C. Geiersbach, M. Hintermüller, Th.M. Surowiec, Risk-averse optimal control of random elliptic VIs, Preprint no. 2962, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2962 .
  Abstract, PDF (1541 kByte)
  We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the stationary points with respect to the penalisation parameter, we obtain two forms of stationarity conditions. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to new challenges unique to the stochastic setting. We also propose a path-following stochastic approximation algorithm using variance reduction techniques and demonstrate the algorithm on a modified benchmark problem.

• G. Dong, M. Hintermüller, K. Papafitsoros, K. Völkner, First-order conditions for the optimal control of learning-informed nonsmooth PDEs, Preprint no. 2940, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2940 .
  Abstract, PDF (408 kByte)
  In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks. The optimal control problem is studied in detail. In particular, the existence and uniqueness of the state equation are shown, and continuity as well as directional differentiability properties of the corresponding control-to-state map are established. Based on approximation capabilities of the pertinent networks, we address fundamental questions regarding approximating properties of the learning-informed control-to-state map and the solution of the corresponding optimal control problem. Finally, several stationarity conditions are derived based on different notions of generalized differentiability.

• M. Hintermüller, T. Keil, Strong stationarity conditions for the optimal control of a Cahn--Hilliard--Navier--Stokes system, Preprint no. 2924, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2924 .
  Abstract, PDF (290 kByte)
  This paper is concerned with the distributed optimal control of a time-discrete Cahn-Hilliard-Navier-Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a variational inequality of fourth order and the Navier-Stokes equation. The existence of solutions to the primal system and of optimal controls is established. The Lipschitz continuity of the constraint mapping is derived and used to characterize the directional derivative of the constraint mapping via a system of variational inequalities and partial differential equations. Finally, strong stationarity conditions are presented following an approach from Mignot and Puel.

Vorträge, Poster

• M. Hintermüller, A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives, SIAM Conference on Computational Science and Engineering (CSE23), MS390 ``Algorithms for Applications in Nonconvex, Nonsmooth Optimization'', February 26 - March 3, 2023, Amsterdam, Netherlands, March 3, 2023.

• C. Sirotenko, Machine Learning for Quantitative MRI, Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization, WIAS, January 26, 2023.

• S. Essadi, Constrained deterministic non-smooth mean field games, GAMM 92nd Annual Meeting 2022, August 15 - 19, 2022, RWTH Aachen University, August 16, 2022.

• S. Essadi, Constrained mean field games: analysis and algorithms, SPP1962 Annual Meeting 2022, October 24 - 26, 2022, Novotel Hotel Berlin Mitte, October 25, 2022.

• A. Alphonse, Directional differentiability and optimal control for quasi-variational inequalities (online talk), ``Partial Differential Equations and their Applications'' Seminar, University of Warwick, Mathematics Institute, UK, January 25, 2022.

• A. Alphonse, Risk-averse optimal control of elliptic random variational inequalities, SPP1962 Annual Meeting 2022, October 24 - 26, 2022, Novotel Hotel Berlin Mitte, October 25, 2022.

• M. Bongarti, Boundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundary, Waves Conference 2022, July 24 - 29, 2022, ENSTA Institut Polytechnique de Paris, France, July 25, 2022.

• M. Bongarti, Boundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundary, IFIP TC7 System Modeling and Optimization, July 4 - 8, 2022, University of Technology, Warschau, Poland, July 4, 2022.

• M. Bongarti, Nonlinear gas transport on a network of pipelines, IFIP TC7 System Modeling and Optimization, July 4 - 8, 2022, University of Technology, Warschau, Poland, July 4, 2022.

• M. Bongarti, Boundary stabilization of nonlinear dynamics of acoustics waves under the JMGT equation (online talk), Early Career Math Colloquium, University of Arizona, Tucson, USA, October 12, 2022.

• J.C. De Los Reyes, Bilevel learning for inverse problems, Seminar SFB 1060, April 11 - 14, 2022, Universität Bonn, Fachbereich Mathematik, Bonn, April 14, 2022.

• J. Leake, Lorentzian polynomials on cones and the Heron--Rota--Welsh conjecture, Workshop "Laguerre-Polya Class and Combinatorics", Mathematisches Forschungsinstitut Oberwolfach, March 18, 2022.

• J. Leake, Lorentzian polynomials on cones and the Heron--Rota--Welsh conjecture, TU Braunschweig, June 16, 2022.

• M. Theiss, Constrained MFG: analysis and algorithms, SPP1962 Annual Meeting 2022, October 24 - 26, 2022, Novotel Hotel Berlin Mitte, October 25, 2022.

• M. Brokate, Derivatives of hysteresis operators, MURPHYS 2022, Silesian University in Opava, Czech Republic, May 30, 2022.

• M. Brokate, Newton derivatives of convex functionals, Conference on Multiple Scale Systems, Silesian University in Opava, Ostravice, Czech Republic, January 16, 2022.

• M. Brokate, Rate independent evolutions, Kolloquiumsvortrag, Charles University, Prag, Czech Republic, March 10, 2022.

• M. Brokate, Rate independent evolutions: derivatives and control, Kolloquiumsvortrag, Universität Kiel, April 29, 2022.

• M. Brokate, Strong stationarity for an optimal control problem for a rate independent evolution, Equadiff 15, Masaryk University, Brno, Czech Republic, July 12, 2022.

• H. Kremer, J.-J. Zhu, K. Muandet, B. Schölkopf, Functional generalized empirical likelihood estimation for conditional moment restrictions, ICML 2022: 39th International Conference on Machine Learning (Online Event), Baltimore, USA, July 18 - 23, 2022.

• C. Geiersbach, Optimality conditions and regularization for stochastic optimization with almost sure state constraints, 15th Viennese Conference on Optimal Control and Dynamic Games, July 12 - 15, 2022, TU Wien, Austria, July 14, 2022.

• C. Geiersbach, Optimality conditions and regularization for stochastic optimization with almost sure state constraints, International Conference on Continuous Optimization -- ICCOPT/MOPTA 2022, Cluster ``PDE-Constrained Optimization'', July 23 - 28, 2022, Lehigh University, Bethlehem, Pennsylvania, USA, July 26, 2022.

• C. Geiersbach, Optimization with almost sure state constraints, GAMM 92nd Annual Meeting 2022, RWTH Aachen University, August 16, 2022.

• C. Geiersbach, Game-theoretical modeling for green hydrogen markets, Future WiNS: New Energies for a Sustainable World, December 7 - 9, 2022, Humoldt-Universität zu Berlin, December 9, 2022.

• C. Geiersbach, Optimality conditions and regularization for OUU with almost sure state constraints (online talk), SIAM Conference on Uncertainty Quantification (Hybrid Event), Minisymposium 24 ``PDE-Constrained Optimization Under Uncertainty'', April 12 - 15, 2022, Atlanta, Georgia, USA, April 12, 2022.

• C. Geiersbach, Optimality conditions and regularization for stochastic optimization with almost sure state constraints (online talk), 2022 SIAM Conference on Imaging Science (IS22) (Online Event), Minisymposium ``Stochastic Iterative Methods for Inverse Problems'', March 21 - 25, 2022, March 25, 2022.

• C. Geiersbach, Problems and challenges in stochastic optimization (online talk), WIAS Days, March 2, 2022.

• C. Geiersbach, Shape optimization under uncertainty: Challenges and algorithms, Helmut Schmidt Universität Hamburg, Mathematik im Bauingenieurwesen, April 26, 2022.

• C. Geiersbach, State constraints in stochastic optimization, PGMO days 2022, EDF Lab Paris-Saclay, Palaiseau, France, November 30, 2022.

• M. Bongarti, Boundary stabilization of nonlinear dynamics of acoustic waves under the JMGT equation, Oberseminar Partielle Differentialgleichungen, Universität Konstanz, November 17, 2022.

• M. Hintermüller, A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives (online talk), Workshop 2: Structured Optimization Models in High-Dimensional Data Analysis, December 12 - 16, 2022, National University of Singapore, Institute for Mathematical Sciences, December 15, 2022.

• M. Hintermüller, Optimization subject to learning informed PDEs, International Conference on Continuous Optimization -- ICCOPT/MOPTA 2022, Cluster ``PDE-Constrained Optimization'', July 23 - 28, 2022, Lehigh University, Bethlehem, Pennsylvania, USA, July 27, 2022.

• M. Hintermüller, Optimization with learning-informed differential equation constraints (online talk), Workshop on Control Problems (Online Event), October 17, 2022 - February 20, 2023, Technische Universität Dortmund, October 17, 2022.

• M. Hintermüller, Optimization with learning-informed differential equations, Robustness and Resilience in Stochastic Optimization and Statistical Learning: Mathematical Foundations, May 20 - 24, 2022, Ettore Majorana Foundation and Centre for Scientific Culture, Erice, Italy, May 24, 2022.

• M. Hintermüller, PDE-constrained optimization with learning-informed structures (online talk), Optimization in Oslo (OiO) Seminar, Simula Research Laboratory, Norway, December 7, 2022.

• K. Papafitsoros, Automatic distributed parameter selection of regularization functionals via bilevel optimization (online talk), SIAM Conference on Imaging Science (Online Workshop), Minisymposium ``Statistics and Structure for Parameter and Image Restoration'', March 21 - 25, 2022, March 22, 2022.

• K. Papafitsoros, Total variation methods in image reconstruction, Institute Colloquium, Foundation for Research and Technology Hellas (IACM-FORTH), Institute of Applied and Computational Mathematics, Heraklion, Greece, May 3, 2022.

• K. Papafitsoros, Optimization with learning-informed nonsmooth differential equation constraints, Second Congress of Greek Mathematicians SCGM-2022, Session Numerical Analysis & Scientific Computing, July 4 - 8, 2022, National Technical University of Athens, July 6, 2022.

• C. Sirotenko, Dictionary learning for an in inverse problem in quantitative mri, GAMM 92nd Annual Meeting 2022, RWTH Aachen University, August 16, 2022.

• C. Sirotenko, Dictionary learning for an inverse problem in quantitative MRI (online talk), SIAM Conference on Imaging Science (Online Workshop), Minisymposium ``Recent Advances of Inverse Problems in Imaging'', March 21 - 25, 2022, March 25, 2022.

Preprints im Fremdverlag

• M. Brokate, C. Christof, Strong stationarity conditions for optimal control problems governed by a rate-ndependent Evolution Variational Inequality, Preprint no. arXiv:2205.01196, Cornell University Library, arXiv.org, 2022, DOI 10.48550/arXiv.2205.01196 .