Subdifferential representation of convex functions: Refinements and applications

Joël Benoist, Aris Daniilidis

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)255-265
JournalJournal of Convex Analysis
Volume12
Issue number2
Publication statusPublished - 1 Dec 2005

Keywords

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

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