A characterization of quasiconvex vector-valued functions

Authors:
Joël Benoist, Jonathan M. Borwein and Nicolae Popovici

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1109-1113

MSC (2000):
Primary 26B25; Secondary 90C29

Published electronically:
November 6, 2002

MathSciNet review:
1948101

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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**Joël Benoist**

Affiliation:
LACO, UPRESSA 6090, Department of Mathematics, University of Limoges, 87060 Limoges, France

Email:
benoist@unilim.fr

**Jonathan M. Borwein**

Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Email:
borwein@cecm.sfu.ca

**Nicolae Popovici**

Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University of Cluj, 3400 Cluj-Napoca, Romania

Email:
popovici@math.ubbcluj.ro

DOI:
https://doi.org/10.1090/S0002-9939-02-06761-8

Keywords:
Quasiconvex vector-valued functions,
scalarization,
polar cones

Received by editor(s):
July 7, 2001

Published electronically:
November 6, 2002

Additional Notes:
The second author’s research was supported by NSERC and by the Canada Research Chair Programme

The third author’s research was supported by CNCSIS Romania under Grant no. 1066/2001

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society