Subdifferential representation of convex functions: Refinements and applications

Joël Benoist; Aris Daniilidis

Subdifferential representation of convex functions: Refinements and applications

Joël Benoist, Aris Daniilidis

Department of Mathematics

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

7 Citations (Scopus)

Abstract

Every lower semicontinuous convex function can be represented through its subdifferential by means of an "integration" formula introduced in [10] by Rockafellar. We show that in Banach spaces with the Radon-Nikodym property this formula can be significantly refined under a standard coercivity assumption. This yields an interesting application to the convexification of lower semicontinuous functions. © Heldermann Verlag.

Original language	English
Pages (from-to)	255-265
Journal	Journal of Convex Analysis
Volume	12
Issue number	2
Publication status	Published - 1 Dec 2005

Keywords

Convex function
Cusco mapping
Epi-pointed function
Strongly exposed point
Subdifferential

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AU - Daniilidis, Aris

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N2 - Every lower semicontinuous convex function can be represented through its subdifferential by means of an "integration" formula introduced in [10] by Rockafellar. We show that in Banach spaces with the Radon-Nikodym property this formula can be significantly refined under a standard coercivity assumption. This yields an interesting application to the convexification of lower semicontinuous functions. © Heldermann Verlag.

AB - Every lower semicontinuous convex function can be represented through its subdifferential by means of an "integration" formula introduced in [10] by Rockafellar. We show that in Banach spaces with the Radon-Nikodym property this formula can be significantly refined under a standard coercivity assumption. This yields an interesting application to the convexification of lower semicontinuous functions. © Heldermann Verlag.

KW - Convex function

KW - Cusco mapping

KW - Epi-pointed function

KW - Strongly exposed point

KW - Subdifferential

M3 - Article

VL - 12

SP - 255

EP - 265

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

SN - 0944-6532

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