Necessary optimality conditions of a D.C. set valued bilevel optimization problem

In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdifferential of a cone-convex set valued mapping introduced by Baier and Jahn [6] and the weak subdifferential of a cone-convex set valued mapping of Sawaragi and Tanino [28]. The bilevel set valued problem is transformed into a one level set valued optimization problem using a transformation originated by Ye and Zhu [34]. An example which illustrate the usefulness of our result is also given.