Abstract

We study the existence of residual sets of certain classes of convex functions on a normed linear space. Such sets play an important role in many optimization algorithms for which elements of a certain class can be used as good approximants of given convex functions and thus the abundance of such elements is crucial for the aforementioned algorithms.

Author information

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

Simeon Reich

Dept. of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel

sreich@technion.ac.il

Alexander J. Zaslavski

Dept. of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel

ajzasl@technion.ac.il

Keywords

  • Baire category
  • convex function
  • local uniform convexity
  • lower semi-continuity
  • normed space
  • residual set
  • strict convexity
  • uniformity

Mathematics Subject Classification

46N10, 54E50, 54E52

Suggested citation

K. Barshad, S. Reich, A. J. Zaslavski. “Residuality Properties of Certain Classes of Convex Functions on Normed Linear Spaces.” Journal of Convex Analysis 29 (2022), No. 3, 795–806.

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