Duality for Closed Convex Functions and Evenly Convex Functions

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

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)985-997
JournalJournal of Optimization Theory and Applications
Volume167
Issue number3
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • Closed convex function
  • Evenly convex function
  • Moreau conjugation

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