Necessary and Sufficient Conditions for the Existence of a Global Maximum for Convex Functions in Reflexive Banach Spaces

Abstract

In this note 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 on Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X.

Cite this paper

@inproceedings{ErnstNecessaryAS, title={Necessary and Sufficient Conditions for the Existence of a Global Maximum for Convex Functions in Reflexive Banach Spaces}, author={Emil Ernst and Michel Th{\'e}ra} }