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.

DOI: 10.1051/cocv/2014024

Keywords: Second-order sufficient conditions, optimal control of variational inequalities, bouligand differentiability

^{1}; Meyer, Christian

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@article{COCV_2015__21_1_271_0, author = {Betz, Thomas and Meyer, Christian}, title = {Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {271--300}, publisher = {EDP-Sciences}, volume = {21}, number = {1}, year = {2015}, doi = {10.1051/cocv/2014024}, zbl = {1311.49017}, mrnumber = {3348423}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014024/} }

TY - JOUR AU - Betz, Thomas AU - Meyer, Christian TI - Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 271 EP - 300 VL - 21 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014024/ DO - 10.1051/cocv/2014024 LA - en ID - COCV_2015__21_1_271_0 ER -

%0 Journal Article %A Betz, Thomas %A Meyer, Christian %T Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 271-300 %V 21 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014024/ %R 10.1051/cocv/2014024 %G en %F COCV_2015__21_1_271_0

Betz, Thomas; Meyer, Christian. Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 1, pp. 271-300. doi : 10.1051/cocv/2014024. http://archive.numdam.org/articles/10.1051/cocv/2014024/

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