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A characterization of quasiconvex vector-valued functions
Author(s):
Joël
Benoist;
Jonathan
M.
Borwein;
Nicolae
Popovici
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1109-1113.
MSC (2000):
Primary 26B25;
Secondary 90C29
Posted:
November 6, 2002
MathSciNet review:
1948101
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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  .
References:
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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, Babes-Bolyai University of Cluj, 3400 Cluj-Napoca, Romania
Email:
popovici@math.ubbcluj.ro
DOI:
10.1090/S0002-9939-02-06761-8
PII:
S 0002-9939(02)06761-8
Keywords:
Quasiconvex vector-valued functions,
scalarization,
polar cones
Received by editor(s):
July 7, 2001
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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