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 $\mathbb {R}^n$.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, Babeş-Bolyai University of Cluj, 3400 Cluj-Napoca, Romania
- Email: popovici@math.ubbcluj.ro
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1109-1113
- MSC (2000): Primary 26B25; Secondary 90C29
- DOI: https://doi.org/10.1090/S0002-9939-02-06761-8
- MathSciNet review: 1948101