Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions

In this paper we consider an optimal control problem governed by a rate-independent variational inequality arising in quasistatic plasticity with linear kinematic hardening. Since the solution operator of a variational inequality is not differentiable, the KKT system is not a necessary optimality condition. We show a system of weakly stationary type by passing to the limit with the optimality system of a regularized and time-discretized problem.