Optimization of second order evolution differential inclusions problem with phase constraints

Abstract

In this paper, we obtain optimality conditions for a problem of convex and non-convex second order evolution differential inclusions with phase constraints. Beginning with second order discrete inclusions problem, we derive necessary and sufficient optimality conditions for the discrete case. We use Locally Dual Mapping definition to derive necessary and sufficient conditions for the optimality of the discrete approximation problem. We prove equivalence theorems in order to obtain a relation between discrete approximation and continuous problems. Passing to the limit, sufficient conditions to the continuous optimal problem are established.