  The paper is concerned with an optimal control problem governed by the
rate-independent system of quasi-static perfect elasto-plasticity. The
objective is optimize the displacement field in the domain occupied by the body
by means of prescribed Dirichlet boundary data, which serve as control
variables. The arising optimization problem is nonsmooth for several reasons,
in particular, since the control-to-state mapping is not single-valued. We
therefore apply a Yosida regularization to obtain a single-valued
control-to-state operator. Beside the existence of optimal solutions, their
approximation by means of this regularization approach is the main subject of
this work. It turns out that a so-called reverse approximation guaranteeing the
existence of a suitable recovery sequence can only be shown under an additional
smoothness assumption on at least one optimal solution.
