Optimal Control of Elliptic Variational-Hemivariational Inequalities
Optimal Control of Elliptic Variational-Hemivariational Inequalities
复制标题
椭圆变分-半变分不等式的最优控制
DOI：
10.1007/s10957-018-1303-8
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发表时间：
2018
影响因子：
1.9
通讯作者：
Kunisch Karl
中科院分区：
文献类型：
--
作者：
Peng Zijia;Kunisch Karl
本文讨论了一类由非线性椭圆包含和非光滑代价泛函所支配的最优控制问题的最优性系统。描述状态的系统由变分-半变分不等式组成，证明了该不等式关于控制的解映射是弱闭的。最优控制问题的最优对的存在性。基于自适应罚方法和非光滑分析技巧，得到了近似结果和抽象的一阶最优性必要条件。此外，还给出了一类具有非单调扰动的障碍问题的最优性系统。
This paper deals with the optimality system of an optimal control problem governed by a nonlinear elliptic inclusion and a nonsmooth cost functional. The system describing the state consists of a variational–hemivariational inequality, the solution mapping of which with respect to the control is proved to be weakly closed. Existence of optimal pairs for the optimal control problem is obtained. Approximation results and abstract necessary optimality conditions of first order are derived based on the adapted penalty method and nonsmooth analysis techniques. Moreover, the optimality system for a class of obstacle problems with nonmonotone perturbation is given.