Optimal control of elastic vector-valued Allen-Cahn variational inequalities

Abstract

In this paper we consider a elastic vector-valued Allen-Cahn MPCC
(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.