Stephan Walther
Published 2021-02-04Version 1
The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.
A bundle method using two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator
Limits of sequences of maximal monotone operators
Convergence of inertial dynamics and proximal algorithms governed by maximal monotone operators
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