Convex functions with continuous epigraph or continuous level sets

P. Coutat, M. Volle, J. E. Martinez-Legaz

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functional in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.
Original languageEnglish
Pages (from-to)365-379
JournalJournal of Optimization Theory and Applications
Volume88
DOIs
Publication statusPublished - 1 Jan 1996

Keywords

  • Coercivity
  • Continuous convex sets
  • Convex duality
  • Recession cones
  • Support functions

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