B- and Strong Stationarity for Optimal Control of Static Plasticity with Hardening

Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The controlto-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly stationary type.