Hannes Meinlschmidt ; Christian Meyer ; Stephan Walther - Optimal control of an abstract evolution variational inequality with application to homogenized plasticity

jnsao:5800 - Journal of Nonsmooth Analysis and Optimization, May 12, 2020, Volume 1 - https://doi.org/10.46298/jnsao-2020-5800
Optimal control of an abstract evolution variational inequality with application to homogenized plasticity

Authors: Hannes Meinlschmidt ORCID-iD; Christian Meyer ; Stephan Walther

    The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone operator. The state equation is uniquely solvable, but the associated solution operator is in general not Gâteaux-differentiable. In order to derive optimality conditions, we therefore regularize the state equation 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 derive necessary and sufficient optimality conditions for the regularized problems. The paper ends with an application of the abstract theory to optimal control of homogenized quasi-static elastoplasticity.


    Volume: Volume 1
    Section: Original research articles
    Published on: May 12, 2020
    Accepted on: May 12, 2020
    Submitted on: October 1, 2019
    Keywords: Mathematics - Optimization and Control,49J27, 49J20, 49K27, 49K20, 74C05

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