Optimization of Second Order Evolution Differential Inclusions Problem with Phase Con- straints

Abstract

In this paper, for a problem second order evolution differential inclusions with phase constraints the op-timality conditions are derived. Necessary and sufficient conditions ensuring the existence of a solution tothe problems for evolution differential inclusions of second order have been studied in recent years. Thereare limited number of articles devoted to the optimization problem of second order evolution differential in-clusions with phase constraints. We apply optimality conditions to problems with geometric constraints andconditions for second order discrete inclusions are proved. We use Locally Dual Mapping definition to derivenecessary and sufficient conditions for the optimality of the discrete approximation problem. Passing to thelimit, sufficient conditions to the optimal problem are established.Keywords: Second order differential inclusion, Locally dual mapping, evolution.