The aim of this paper is to characterize in terms of classical convexity and quasiconvexity of extended real-valued functions those set-valued maps which are K-convex or K-quasiconvex with respect to a convex cone K. In particular, we recover some known characterizations of K-convex and...

A a set-valued optimization problem min C F(x), x ∈X 0 , is considered, where X 0 ⊂ X, X and Y are normed spaces, F: X 0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x 0 ,y 0 ), y 0 ∈F(x 0 ), and are called...