An Optimal Control Problem Governed by Quasi-Linear Variational Inequalities

Abstract

An optimal control problem governed by quasi-linear variational inequality is considered. The cost functional to be minimized contains the solution of a quasi-linear variational inequality. To get the existence, regularity, and necessary condition for the optimal pair, a new related control problem is introduced. By proving the existence of an optimal pair to such a new problem, the existence and regularity of the optimal pair to the original problem are obtained. It turns out that the regularity obtained is sharp in general. Some necessary conditions of the optimal pair are also obtained.