Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening

Betz, Thomas; Meyer, Christian

ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 271-300

The paper is concerned with the optimal control of static elastoplasticity with linear kinematic hardening. This leads to an optimal control problem governed by an elliptic variational inequality (VI) of first kind in mixed form. Based on $L^p$-regularity results for the state equation, it is shown that the control-to-state operator is Bouligand differentiable. This enables to establish second-order sufficient optimality conditions by means of a Taylor expansion of a particularly chosen Lagrange function.

Classification : 49K20, 74C05, 74P10, 35R45
Keywords: Second-order sufficient conditions, optimal control of variational inequalities, bouligand differentiability

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