Necessary conditions for solutions of set optimization problems with respect to variable domination structures / E. Kobis, L. Th. Tam, Chr. Tammer and J.-Ch. Yao

Abstract

Abstract: In this chapter, we introduce several set relations equipped with a variable domination structure, which is not necessarily given by a cone-valued map. We also derive the relationships between the solution concepts for set optimization problems given by set approach and vector approach. The main part of this chapter is devoted to investigate necessary optimality conditions for solutions of set optimization problems based on set approach. These necessary optimality conditions are derived in terms of Mordukhovich’s coderivative for optimal solutions of set-valued problems with respect to various set order relations.