Abstract
In this article, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1–3,14,15,32] 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 Citation6 and the weak subdifferential of a cone-convex set-valued mapping of Sawaragi and Tanino Citation28. The bilevel set-valued problem is transformed into a one level set-valued optimization problem using a transformation originated by Ye and Zhu Citation34. An example illustrating the usefulness of our result is also given.
Acknowlegements
This work has been done during the N. Gadhi's stay at the TU Bergakademie Freiberg as a research fellow of the Alexander von Humboldt foundation.