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search.filters.applied.f.access: openAccess × Author: Hintermüller, Michael × Start date: 2017 × DDC: 510 × Has files: Yes × Subject: PDE-constrained optimization ×

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    Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Gahururu, Deborah; Hintermüller, Michael; Stengl, Steven-Marian; Surowiec, Thomas M.
    PDE-constrained (generalized) Nash equilibrium problems (GNEPs) are considered in a deterministic setting as well as under uncertainty. This includes a study of deterministic GNEPs with nonlinear and/or multivalued operator equations as forward problems and PDE-constrained GNEPs with uncertain data. The deterministic nonlinear problems are analyzed using the theory of generalized convexity for set-valued operators, and a variational approximation approach is proposed. The stochastic setting includes a detailed overview of the recently developed theory and algorithms for risk-averse PDE-constrained optimization problems. These new results open the way to a rigorous study of stochastic PDE-constrained GNEPs.
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    Optimization of a multiphysics problem in semiconductor laser design
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.
    A @multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a Ge-on-Si microbridge are given. The highly favorable electronic properties of this design are demonstrated by steady-state simulations of the corresponding van Roosbroeck (drift-diffusion) system.
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    On the convexity of optimal control problems involving non-linear PDEs or VIs and applications to Nash games (changed title: Vector-valued convexity of solution operators with application to optimal control problems)
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Hintermüller, Michael; Stengl, Steven-Marian
    Generalized Nash equilibrium problems in function spaces involving PDEs are considered. One of the central issues arising in this context is the question of existence, which requires the topological characterization of the set of minimizers for each player of the associated Nash game. In this paper, we propose conditions on the operator and the functional that guarantee the reduced formulation to be a convex minimization problem. Subsequently, we generalize results of convex analysis to derive optimality systems also for non-smooth operators. Our theoretical findings are illustrated by examples.