SIAM Journal on Control and Optimization, Vol.54, No.1, 129-152, 2016
OPTIMAL CONTROL OF ELASTIC VECTOR-VALUED ALLEN-CAHN VARIATIONAL INEQUALITIES
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.
Keywords:vector-valued Allen-Cahn system;parabolic obstacle problems;linear elasticity;MPCCs;mathematical programs with complementarity constraints;optimality conditions