Abstract

We prove that every proper convex and lower semicontinuous functional Φ defined on a real reflexive Banach space X is semicoercive if and only if every small uniform perturbation of Φ attains its minimum value on X.

Author information

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

Samir Adly

LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges, France

Emil Ernst

Institute of Mathematics, Romanian Academy of Sciences, 70700 Bucharest, Romania

Michel Théra

Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges, France

Keywords

  • Convex analysis
  • barrier cone
  • support functional
  • recession analysis
  • semicoercive functional

Mathematics Subject Classification

49J40

Suggested citation

S. Adly, E. Ernst, M. Théra. “A Characterization of Convex and Semicoercive Functionals.” Journal of Convex Analysis 8 (2001), No. 1, 127–148.

Copyright Heldermann Verlag 2001