A characterization of quasiconvex vector-valued functions

The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are Κ-quasiconvex with respect to a closed convex cone Κ in a Banach space. Our main result extends a wellknown characterization of Κ-quasiconvexity by means of extreme directions of the polar cone of Κ, obtained by Dinh The Luc in the particular case when Κ is a polyhedral cone generated by exactly n linearly independent vectors in the Euclidean space ℝⁿ.