THE EXISTENCE RESULTS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY QUASI-VARIATIONAL INEQUALITIES IN REFLEXIVE BANACH SPACES

Abstract

In this paper, some existence results for optimal control problems governed by abstract quasi-variational inequalities are proved in reflexive Banach spaces. As an application, an existence of the optimal control for the bilateral obstacle optimal control problem is also given under some suitable conditions, in which the state satisfies a quasilinear elliptic variational inequality with a source term.