Existence theorem and optimality conditions for a class of convex semi-infinite problems with noncompact index sets

Abstract

The paper is devoted to study of a special class of semi-infinite problems arising in nonlinear parametric Semi-infinite Programming, when the differential properties of the solutions are being studied. These problems are convex and possess non-compact index sets. In the paper, we present conditions guaranteeing the existence of optimal solutions, and prove new optimality criterion. An example illustrating the obtained results is presented.