CONVEXITY IN THE FRAMEWORK OF VARIABLE DOMINATION STRUCTURES AND APPLICATIONS IN OPTIMIZATION

摘要

In this paper, we investigate convexity of set-valued mappings. Our new concepts are based on several set relations w.r.t. variable domination structures. Applying some appropriate properties of these structures, we obtain the relationships between convexity of a set-valued mapping and convexity of its epigraph. In addition, we study convexity of scalarizing functionals used in vector (and set-) optimization w.r.t. variable domination structures. Optimality conditions for nondominated (minimal) solutions for vector optimization problems with respect to variable domination structures in terms of limiting (Mordukhovich) subdifferential are derived.