SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2498-2523, January 2021.
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 (resp., vanishing viscosity approach) 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.

中文翻译：

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完美塑性的最优控制第二部分：位移跟踪

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2498-2523 页，2021 年 1 月。
该论文涉及由准静态完美弹塑性的速率无关系统控制的最优控制问题。目标是通过指定的 Dirichlet 边界数据作为控制变量来优化物体占据的域中的位移场。由于多种原因，出现的优化问题是不平滑的，特别是因为控制到状态的映射不是单值的。因此，我们应用 Yosida 正则化（相应地，粘度消失方法）来获得单值控制到状态算子。除了存在最优解之外，通过这种正则化方法来逼近它们是这项工作的主要主题。