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

Cite this

@article{f998c1386e8e42c7aa73b398fb7e07fe,

title = "Subdifferential representation of convex functions: Refinements and applications",

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. {\textcopyright} Heldermann Verlag.",

keywords = "Convex function, Cusco mapping, Epi-pointed function, Strongly exposed point, Subdifferential",

author = "Jo{\"e}l Benoist and Aris Daniilidis",

year = "2005",

month = dec,

day = "1",

language = "English",

volume = "12",

pages = "255--265",

journal = "Journal of Convex Analysis",

issn = "0944-6532",

publisher = "Heldermann Verlag",

number = "2",

}

TY - JOUR

T1 - Subdifferential representation of convex functions: Refinements and applications

AU - Benoist, Joël

AU - Daniilidis, Aris

PY - 2005/12/1

Y1 - 2005/12/1

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

IS - 2

ER -

Subdifferential representation of convex functions: Refinements and applications

Abstract

Keywords

Fingerprint

Cite this