Convex functions with continuous epigraph or continuous level sets

P. Coutat; M. Volle; J. E. Martinez-Legaz

doi:https://doi.org/10.1007/BF02192176

Convex functions with continuous epigraph or continuous level sets

P. Coutat, M. Volle, J. E. Martinez-Legaz

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functional in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.

Original language	English
Pages (from-to)	365-379
Journal	Journal of Optimization Theory and Applications
Volume	88
DOIs	https://doi.org/10.1007/BF02192176
Publication status	Published - 1 Jan 1996

Keywords

Coercivity
Continuous convex sets
Convex duality
Recession cones
Support functions

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AU - Volle, M.

AU - Martinez-Legaz, J. E.

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N2 - Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functional in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.

AB - Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functional in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.

KW - Coercivity

KW - Continuous convex sets

KW - Convex duality

KW - Recession cones

KW - Support functions

U2 - https://doi.org/10.1007/BF02192176

DO - https://doi.org/10.1007/BF02192176

M3 - Article

VL - 88

SP - 365

EP - 379

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

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