Optimization of semilinear delay-differential inclusions in infinite-dimensional spaces

This paper is devoted to the study of optimization problems described by a class of semilinear delay-differential inclusions in infinite-dimensional spaces. First, we construct a sequence of discrete-time problems that approximates to the continuous-time problems. Then, we derive necessary optimality conditions for the discrete-time problems by reducing them to a mathematical programming problem in infinite-dimensional spaces. Finally, we establish necessary optimality conditions for the original problem by passing to the limit in the necessary optimality conditions for discrete-time problems.