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

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 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 illustrating the usefulness of our result is also given.

Keywords: Bilevel optimization; Karush-Kuhn-Tucker multipliers; necessary optimality conditions; separation principle; set-valued mappings; sub-differential; weak subdifferential; support function

Document Type: Research article

DOI: 10.1080/02331930701761508

Affiliations: 1: Department of Mathematics and Computers Sciences, Technical University Bergakademie Freiberg, Freiberg, Germany 2: Department of Mathematics, Sidi Mohamed Ben Abdellah University, Dhar El Mehrez, Fes, Morocco