An Approximating Approach to an Optimal Control Problem for an Elliptic Variational Inequality on a Mixed Boundary⋆. (4th July 2022) - Duan, Yarui; Wu, Pengcheng; Zhou, Yuying
Abstract: In this article, an optimal control problem (OCP) for a system governed by a class of double obstacle elliptic variational inequalities on a mixed boundary is proposed. An approximating optimal control problem ( OCP ) ε is then defined to approximate the original problem (OCP) by a penalty method. Under some assumptions, the existence result for the problem ( OCP ) ε is proved. The sequence of solutions to the problem ( OCP ) ε converges to a solution of the original problem (OCP) as the penalty parameter tends to zero. Next, the necessary optimality conditions are obtained for the solution of the problem ( OCP ) ε with a given concrete penalty function. At last, an algorithm is used to solve a given concrete optimal control problem. Numerical experimental results are presented to show that the approximation method is effective and practical.