A characterization of quasiconvex vector-valued functions

Benoist, Joël; Borwein, Jonathan; Popovici, Nicolae

doi:10.1090/S0002-9939-02-06761-8

A characterization of quasiconvex vector-valued functions
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by Joël Benoist, Jonathan M. Borwein and Nicolae Popovici PDF

Proc. Amer. Math. Soc. 131 (2003), 1109-1113 Request permission

Abstract:

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

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