Duality for Closed Convex Functions and Evenly Convex Functions

M. Volle; J. E. Martínez-Legaz; J. Vicente-Pérez

doi:10.1007/s10957-013-0395-4

Duality for Closed Convex Functions and Evenly Convex Functions

M. Volle, J. E. Martínez-Legaz, J. Vicente-Pérez

Department of Economics and Economic History

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

4 Citations (Scopus)

Abstract

© 2013, Springer Science+Business Media New York. We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of h that are either continuous affine or closed (respectively, open) halfspaces valley functions.

Original language	English
Pages (from-to)	985-997
Journal	Journal of Optimization Theory and Applications
Volume	167
Issue number	3
DOIs	https://doi.org/10.1007/s10957-013-0395-4
Publication status	Published - 1 Dec 2015

Keywords

Closed convex function
Evenly convex function
Moreau conjugation

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AU - Volle, M.

AU - Martínez-Legaz, J. E.

AU - Vicente-Pérez, J.

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Y1 - 2015/12/1

N2 - © 2013, Springer Science+Business Media New York. We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of h that are either continuous affine or closed (respectively, open) halfspaces valley functions.

AB - © 2013, Springer Science+Business Media New York. We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of h that are either continuous affine or closed (respectively, open) halfspaces valley functions.

KW - Closed convex function

KW - Evenly convex function

KW - Moreau conjugation

U2 - 10.1007/s10957-013-0395-4

DO - 10.1007/s10957-013-0395-4

M3 - Article

VL - 167

SP - 985

EP - 997

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

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