Abstract

We prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X.

Author information

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

Emil Ernst

Lab. de Modélisation en Mécanique et Thermodynamique, Université Paul Cezanne, Fac. des Sciences et Techniques, Casse 322, Av. Esc. Normandie-Niemen, 13397 Marseille

Emil.Ernst@univ.u-3mrs.fr

Michel Théra

Projet MOD (XLIM, UMR-CNRS 6172), Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France

michel.thera@unilim.fr

Keywords

  • Global maximum of a convex function
  • optimality conditions

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Suggested citation

E. Ernst, M. Théra. “Global Maximum of a Convex Function: Necessary and Sufficient Conditions.” Journal of Convex Analysis 13 (2006), No. 3/4, 687–694. https://doi.org/10.68381/jca13051

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