Publications

Monographs

  • 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 .

  • 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. 213--270, (Chapter Published), DOI 10.1016/bs.hna.2020.10.003 .

Articles in Refereed Journals

  • 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, published online in Nov. 2022, 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 .

  • 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.

  • 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.

  • 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, (2022), published online on 05.05.2022, 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.

  • M. Bongarti, S. Charoenphon, I. Lasiecka, Vanishing relaxation time dynamics of the Jordan Moore--Gibson--Thompson equation arising in nonlinear acoustics, Journal of Evolution Equations, 21 (2021), pp. 3553--3584, DOI 10.1007/s00028-020-00654-2 .

  • M. Bongarti, I. Lasiecka, R. Triggiani, The SMGT equation from the boundary: Regularity and stabilization, Applicable Analysis. An International Journal, published online on 30.11.2021, DOI 10.1080/00036811.2021.1999420 .

  • M.S. Aronna, J.F. Bonnans, A. Kröner, State constrained control-affine parabolic problems II: Second order sufficient optimality conditions, SIAM Journal on Control and Optimization, 59 (2021), pp. 1628--1655, DOI 10.1137/19M1286906 .

  • R. Bot, G. Dong, P. Elbau, O. Scherzer, Convergence rates of first- and higher-order dynamics for solving linear ill-posed problems, Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, published online on 17.08.2021, DOI 10.1007/s10208-021-09536-6 .

  • G. Dong, M. Hintermüller, Y. Zhang, A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging, SIAM Journal on Imaging Sciences, 14 (2021), pp. 645--688, DOI 10.1137/20M1366277 .
    Abstract
    In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows. We concentrate on two equations: one is a damped second-order total variation flow, which is primarily motivated by the application of image denoising; the other is a damped second-order mean curvature flow for level sets of scalar functions, which is related to a non-convex variational model capable of correcting displacement errors in image data (e.g. dejittering). For the former equation, we prove the existence and uniqueness of the solution. For the latter, we draw a connection between the equation and some second-order geometric PDEs evolving the hypersurfaces which are described by level sets of scalar functions, and show the existence and uniqueness of the solution for a regularized version of the equation. The latter is used in our algorithmic development. A general algorithm for numerical discretization of the two nonlinear PDEs is proposed and analyzed. Its efficiency is demonstrated by various numerical examples, where simulations on the behavior of solutions of the new equations and comparisons with first-order flows are also documented.

  • C. Geiersbach, W. Wollner, Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraints, SIAM Journal on Optimization, 31 (2021), pp. 2455--2480, DOI 10.1137/20M1363558 .

  • C. Geiersbach, E. Loayza-Romero, K. Welker, Stochastic approximation for optimization in shape spaces, SIAM Journal on Optimization, 31 (2021), pp. 348--376, 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. 705--740, DOI 10.1007/s10589-020-00259-y .

  • A. Alphonse, C.N. Rautenberg, J.F. Rodrigues, Analysis of a quasi-variational contact problem arising in thermoelasticity, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 217 (2022), pp. 112728/1--112728/40 (published online on 13.12.2021), 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, published online on 27.10.2021, 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.

  • M. Hintermüller, S.-M. Stengl, Th.M. Surowiec, Uncertainty quantification in image segmentation using the Ambrosio--Tortorelli approximation of the Mumford--Shah energy, Journal of Mathematical Imaging and Vision, 63 (2021), pp. 1095--1117, DOI 10.1007/s10851-021-01034-2 .
    Abstract
    The quantification of uncertainties in image segmentation based on the Mumford-Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio-Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.

  • M. Hintermüller, S. Rösel, Duality results and regularization schemes for Prandtl--Reuss perfect plasticity, ESAIM. Control, Optimisation and Calculus of Variations, 27 (2021), pp. S1/1--S1/32, DOI 10.1051/cocv/2018004 .
    Abstract
    We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual 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 well-defined 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 well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed.

Contributions to Collected Editions

  • 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.

  • J.-J. Zhu, Ch. Kouridi, N. Yassine, B. Schölkopf, Adversarially robust kernel smoothing, in: Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, G. Camps-Valls, F.J.R. Ruiz, I. Valera, eds., 151 of Proceedings of Machine Learning Research, 2022, pp. 4972--4994.
    Abstract
    We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the Wasserstein distance and the maximum mean discrepancy. We adapt the integral operator using supremal convolution in convex analysis to form a novel function majorant used for enforcing robustness. Our method is simple in form and applies to general loss functions and machine learning models. Exploiting a connection with optimal transport, we prove theoretical guarantees for certified robustness under distribution shift. Furthermore, we report experiments with general machine learning models, such as deep neural networks, to demonstrate competitive performance with the state-of-the-art certifiable robust learning algorithms based on the Wasserstein distance.

  • M. Bongarti, I. Lasiecka, Boundary stabilization of the linear MGT equation with feedback Neumann control, in: Deterministic and Stochastic Optimal Control and Inverse Problems, B. Jadamba, A.A. Khan, S. Migórski, M. Sama, eds., CRC Press, Boca Raton, 2021, pp. 150--169, DOI 10.1201/9781003050575 .

  • J.-J. Zhu, W. Jitkrittum, M. Diehl, B. Schölkopf, Kernel distributionally robust optimization: Generalized duality theorem and stochastic approximation, in: Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, A. Banerjee, K. Fukumizu, eds., 130 of Proceedings of Machine Learning Research, 2021, pp. 280--288.

Preprints, Reports, Technical Reports

  • 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.

  • M. Gugat, J. Habermann, M. Hintermüller, O. Huber, Constrained exact boundary controllability of a semilinear model for pipeline gas flow, Preprint no. 2899, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2899 .
    Abstract, PDF (6722 kByte)
    While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.

  • M. Hintermüller, S.-M. Stengl, A generalized $Gamma$-convergence concept for a type of equilibrium problems, Preprint no. 2879, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2879 .
    Abstract, PDF (246 kByte)
    A novel generalization of Γ-convergence applicable to a class of equilibrium problems is studied. After the introduction of the latter, a variety of its applications is discussed. The existence of equilibria with emphasis on Nash equilibrium problems is investigated. Subsequently, our Γ-convergence notion for equilibrium problems, generalizing the existing one from optimization, is introduced and discussed. The work ends with its application to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities.

  • 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, Preprint no. 2871, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2871 .
    Abstract, PDF (319 kByte)
    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.

  • A. Kröner, C.N. Rautenberg, S. Rodrigues, Existence, uniqueness, and stabilization results for parabolic variational inequalities, Preprint no. 2870, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2870 .
    Abstract, PDF (3548 kByte)
    In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau--Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions.

  • C. Geiersbach, M. Hintermüller, Optimality conditions and Moreau--Yosida regularization for almost sure state constraints, Preprint no. 2862, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2862 .
    Abstract, PDF (415 kByte)
    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.

  • M. Brokate, P. Krejčí, A variational inequality for the derivative of the scalar play operator, Preprint no. 2803, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2803 .
    Abstract, PDF (302 kByte)
    We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.

Talks, Poster

  • 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.

  • 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.

  • 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, 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), SIAM Conference on Imaging Science (Online Workshop), 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.

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

  • 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.

  • A. Alphonse, Directional differentiability and optimal control for elliptic quasi-variational inequalities (online talk), Workshop ``Challenges in Optimization with Complex PDE-Systems'' (Hybrid Workshop), February 14 - 20, 2021, Mathematisches Forschungsinstitut Oberwolfach, February 17, 2021.

  • A. Alphonse, Directional differentiability and optimal control for elliptic quasi-variational 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 DFG-PP 1962 Non-smooth and Complementarity-based 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.

  • J. Leake, Continuous maximum entropy distributions (online talk), Optimization Under Symmetry, November 29 - December 3, 2021, University of California at Berkeley, Simons Institute for the Theory of Computing, USA, November 30, 2021.

  • J. Leake, Lorentzian polynomials on cones and the Heron--Rota--Welsh conjecture, Monday Colloquium of Graduiertenkolleg ``Facets of Complexity'' (GRK 2434), Technische Universität Berlin, November 22, 2021.

  • J. Leake, Sampling matrices from HCIZ densities (online talk), Frontiers of Statistical Mechanics and Theoretical Computer Science 2021 (Hybrid Event), December 13 - 15, 2021, University of Illinois at Chicago, USA / Durham University, UK, December 14, 2021.

  • J.C. de Los Reyes, Bilevel learning for inverse problems, Berlin Oberseminar: Optimization, Control and Inverse Problems, WIAS, December 6, 2021.

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

  • C. Geiersbach, Optimal conditions & regularization for stochastic optimization with almost sure state constraints, Vienna Colloquium on Decision Making under Uncertainty, October 1, 2021, Vienna, Austria, October 1, 2021.

  • C. Geiersbach, Optimality conditions and regularization for stochastic optimization with almost sure state constraints, Forschungsseminar Algorithmische Optimierung, Humboldt-Universität zu Berlin, November 18, 2021.

  • C. Geiersbach, Optimality conditions and regularization for stochastic optimization with almost sure state constraints (online talk), Oberseminar Numerical Optimization (Online Event), Universität Konstanz, June 29, 2021.

  • C. Geiersbach, Optimality conditions and regularization for convex stochastic optimization with almost sure state constraints (online talk), Workshop ``Challenges in Optimization with Complex PDE-Systems'' (Hybrid Workshop), February 14 - 20, 2021, Mathematisches Forschungsinstitut Oberwolfach, February 16, 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 for optimization in shape spaces (online talk), International Conference on Spectral and High Order Methods (ICOSAHOM), Session: ``Shape and Topology Optimization'' (Online Event), Technische Universität Wien / Universität Wien, Austria, July 13, 2021.

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

  • G. Dong, M. Hintermüller, K. Papafitsoros, Learning-informed model meets integrated physics-based method in quantitative MRI (online talk), 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics, S21: ``Mathematical Signal and Image Processing'' (Online Event), March 15 - 19, 2021, Universität Kassel, March 18, 2021.

  • G. Dong, A class of second-order quasi-linear PDEs and their applications, 15th International Conference on Free Boundary Problems: Theory and Applications 2021 (FBP 2021, Online Event), September 13 - 17, 2021, WIAS, Berlin, September 16, 2021.

  • G. Dong, Physics-integrated models and data-driven regularization methods for qMRI (online talk), online meeting between Physikalisch-Technische Bundesanstalt (PTB) division 8 and WIAS FG 8 to exchange ideas in quantitative MRI, April 16, 2021.

  • M. Hintermüller, Mathematics of quantitative MRI (online talk), The 5th International Symposium on Image Computing and Digital Medicine (ISICDM 2021), December 17 - 20, 2021, Guilin, China, December 18, 2021.

  • M. Hintermüller, Mathematics of quantitative imaging (online talk), MATH+ Thematic Einstein Semester on Mathematics of Imaging in Real-World Challenges, Berlin, November 12, 2021.

  • M. Hintermüller, Non smooth and complementarity-based distributed parameter systems: Simulation and hierarchical optimization (online talk), 91th Annual Meeting of the International Association of Applied Mathematics and Mechanics (Online Event), Session DFG-PP 1962 Non-smooth and Complementarity-based Distributed Parameter Systems, March 15 - 19, 2021, Universität Kassel, March 16, 2021.

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

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

  • M. Hintermüller, Optimization with learning-informed differential equation constraints and its applications (online talk), Oberseminar Numerical Optimization, Universität Konstanz, Fachbereich Mathematik und Statistik, December 14, 2021.

  • M. Hintermüller, Quantitative imaging: Physics integrated and machine learning based models in MRI (online talk), MATH-IMS Joint Applied Mathematics Colloquium Series, The Chinese University of Hong Kong, Center for Mathematical Artificial Intelligence, China, December 3, 2021.

  • M. Hintermüller, Semi-smooth 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, Semi-smooth 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.

  • A. Kröner, Optimal control and deep learning, Research Seminar: Mathematical Modelling and Simulation, Humboldt-Universität zu Berlin, July 15, 2021.

  • K. Papafitsoros, A. Kofler, Classical vs. data driven regularization methods in imaging (online tutorial), MATH+ Thematic Einstein Semester on Mathematics of Imaging in Real-Word Challenges, Berlin, October 29, 2021.

  • K. Papafitsoros, Automatic distributed regularization parameter selection in total generalized variation based image reconstruction via bilevel optimization (online talk), SIAM Conference on Optimization (Online Event), Minisymposium ``Bilevel Optimization: Theory, Applications and Algorithms'', July 20 - 23, 2021, July 21, 2021.

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

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

  • K. Papafitsoros, Total variation methods in image reconstruction, Departmental Seminar, National Technical University of Athens, Department of Mathematics, Greece, December 21, 2021.

  • C. Sirotenko, What is variational image processing? (online tak), MATH+ Friday Colloquium, ``What is ...'' Seminar, Berlin, July 9, 2021.

  • S.-M. Stengl, Combined regularization and discretization of equilibrium problems and primal-dual gap estimators, Seminar Mathematical Optimization / Non-smooth Variational Problems and Operator Equations, WIAS Berlin, April 15, 2021.

External Preprints

  • V. Grimm, M. Hintermüller, O. Huber, L. Schewe, M. Schmidt, G. Zöttl, A PDE-constrained generalized Nash equilibrium approach for modeling gas markets with transport, Preprint no. 458, Dokumentserver des Sonderforschungsbereichs Transregio 154, urlhttps://opus4.kobv.de/opus4-trr154/home, 2021.

  • V. Pagliari, K. Papafitsoros, B. Ralţă, A. Vikelis, Bilevel training schemes in imaging for total-variation-type functionals with convex integrands, Preprint no. arXiv:2112.10682, Cornell University Library, arXiv.org, 2021.