Abstract

We attempt to characterize the property, for a convex function f , "Epi f is sharp and weakly complete" by a property of the polar function. Some examples show that a result completely analogous to the J.L. Joly characterization of "Epi f is sharp and weakly locally compact" seems impossible. We use an old (1962) result of G. Choquet.

Author information

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

Jean Saint-Pierre

Département de Mathématiques, Case 051, Université Montpellier II, Place Eugène Bataillon, F-34095 Montpellier Cedex 5

Michel Valadier

Département de Mathématiques, Case 051, Université Montpellier II, Place Eugène Bataillon, F-34095 Montpellier Cedex 5

Keywords

  • Weakly complete sets
  • sharp epigraphs
  • locally convex linear spaces
  • duality

Suggested citation

J. Saint-Pierre, M. Valadier. “An Attempt of Characterization of Functions with Sharp Weakly Complete Epigraphs.” Journal of Convex Analysis 1 (1994), No. 1, 101–105. https://doi.org/10.68381/jca01007

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press.