# Second-Order Sufficient Conditions for Optimal Control of Elastoplasticity

Thomas Betz^{*} and Christian Meyer

An optimal control problem governed by an elliptic variational inequality (VI) of first kind in mixed form is considered. This VI models the static problem of infinitesimal elastoplasticity with linear kinematic hardening. An optimization of elastoplastic deformation processes thus leads to the optimal control problem under consideration. It is well known that the control-to-state map associated to VIs is in general not Gateaux-differentiable. The same applies in our particular case. Thus standard techniques to derive optimality conditions for optimal control problems cannot be employed. It can however be shown that the control-to-state operator is Bouligand differentiable. Based on this result, we establish second-order sufficient optimality conditions by means of a Taylor expansion of a particularly chosen Lagrange function.

Mathematics Subject Classification: 49K20 74C05 74P10 35R45

Keywords: Second-order sufficient conditions; optimal control of variational inequalities; Bouligand differentiability

Minisymposion: Optimization of Mechanical Systems