SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2236-2255, January 2020.
This paper deals with the optimal control of an obstacle problem where the control variable is the obstacle. The state system is described by a class of quasilinear elliptic variational inequalities with nonmonotone and nonsmooth perturbations. The cost functional is neither smooth nor convex, but locally Lipschitz continuous. The existence and approximation result of optimal solutions are proved. The optimality system is derived by Lagrange multiplier rules, smooth approximations, and nonsmooth analysis techniques.

中文翻译：

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涉及非光滑成本函数和拟线性变分不等式的最优障碍控制问题

SIAM控制与优化杂志，第58卷，第4期，第2236-2255页，2020年1月。
本文讨论了以控制变量为障碍物的障碍物问题的最优控制。状态系统由一类具有非单调和非光滑摄动的拟线性椭圆变分不等式描述。成本函数既不是平滑的也不是凸的，而是局部的Lipschitz连续的。证明了最优解的存在性和逼近结果。最佳系统是通过拉格朗日乘数规则，平滑近似和非平滑分析技术得出的。