Journal of Optimization Theory and Applications

, Volume 88, Issue 2, pp 365–379

Convex functions with continuous epigraph or continuous level sets

  • P. Coutat
  • M. Volle
  • J. E. Martinez-Legaz
Contributed Papers

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 functionals 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.

Key words

Continuous convex sets support functions convex duality coercivity recession cones 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • P. Coutat
    • 1
  • M. Volle
    • 2
  • J. E. Martinez-Legaz
    • 3
  1. 1.Department of MathematicsUniversity of Paris 1ParisFrance
  2. 2.Department of MathematicsUniversity of AvignonAvignonFrance
  3. 3.Departament d'Economia i d'Història EconòmicaUniversitat Autònoma de BarcelonaBarcelonaSpain

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