A characterization of quasiconvex vector-valued functions
Joël Benoist, Jonathan Michael Borwein, Nicolae Popovici · Proceedings of the American Mathematical Society · 2002
The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are K K -quasiconvex with respect to a closed convex cone K K in a Banach space. Our main result extends a well-known characterization of K K -quasiconvexity by means of extreme directions of the polar cone of K K , obtained by Dinh The Luc in the particular case when K K is a polyhedral cone generated by exactly n n linearly independent vectors in the Euclidean space R n \mathbb {R}^n .