There are many totally convex functions

Dan Butnariu, Simeon Reich, Alexander J. Zaslavski

Research output: Contribution to journalArticlepeer-review


Let K be a convex subset of a normed linear space and let R1 denote the real line. We show that there are many (in the sense of Bake category) strictly convex and totally convex functions f : K → R 1. It is known that the existence of such functions is crucial in numerous optimization algorithms.

Original languageEnglish
Pages (from-to)623-632
Number of pages10
JournalJournal of Convex Analysis
Issue number3-4
StatePublished - 2006


  • Complete metric space
  • Essentially strictly convex function
  • Generic property
  • Strictly convex function
  • Totally convex function

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


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