Authors: Meinlschmidt, Hannes
Meyer, Christian
Walther, Stephan
Title: Optimal control of an abstract evolution variational inequality with application to homogenized plasticity
Language (ISO): en
Abstract: The paper is concerned with an optimal control problem governed by a state equa-tion in form of a generalized abstract operator differential equation involving a maximal monotoneoperator. The state equation is uniquely solvable, but the associated solution operator is in generalnot Gˆateaux-differentiable. In order to derive optimality conditions, we therefore regularize the stateequation and its solution operator, respectively, by means of a (smoothed) Yosida approximation.We show convergence of global minimizers for regularization parameter tending to zero and derivenecessary and sufficient optimality conditions for the regularized problems. The paper ends with anapplication of the abstract theory to optimal control of homogenized quasi-static elastoplasticity.
Subject Headings: optimal control of operator differential equations
Yosida approximation
necessary and sufficient optimality conditions
homogenized plasticity
evolution variational inequality
Issue Date: 2019-09
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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