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In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasi-static plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator, which imply the existence of an optimal control. Moreover, a discretization in time is derived and we show that every local minimizer of the continuous problem can be approximated by minimizers of modified, time-discrete problems. (A correction is attached.)

Optimal Control of Quasi-static Plasticity with Linear Kinematic Hardening, Part I: Existence and Discretization in Time