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<Subscript> C </Subscript> F(x), x ∈X <Subscript>0</Subscript>, is considered, where X <Subscript>0</Subscript> ⊂ X, X and Y are normed spaces, F: X <Subscript>0</Subscript> ⊂ 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 <Superscript>0</Superscript>,y <Superscript>0</Superscript>), y <Superscript>0</Superscript> ∈F(x <Superscript>0</Superscript>), and are called...</superscript></superscript></superscript></superscript></subscript></subscript></subscript></subscript>