Optimal Control of Elastic Vector-Valued Allen--Cahn Variational Inequalities

Abstract

In this paper we consider an elastic vector-valued Allen-Cahn mathematical programs with complementarity constraints problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.