Abstract

Let KK be a convex subset of a normed linear space and let R1R^1 denote the real line. We show that there are many (in the sense of Baire category) strictly convex and totally convex functions f ⁣:K→R1f \colon K \to R^1. It is known that the existence of such functions is crucial in numerous optimization algorithms.

Author information

Contact details are reproduced from the original publication and may be historical.

Alexander J. Zaslavski

Dept. of Mathematics, Technion - Israel Inst. Technology, 32000 Haifa, Israel

ajzasl@tx.technion.ac.il

Keywords

  • Complete metric space
  • essentially strictly convex function
  • generic property
  • strictly convex function
  • totally convex function

Mathematics Subject Classification

46N10, 52A41, 54E50, 54E52

Suggested citation

D. Butnariu, S. Reich, A. J. Zaslavski. “There are Many Totally Convex Functions.” Journal of Convex Analysis 13 (2006), No. 3/4, 623–632. https://doi.org/10.68381/jca13048

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press.