Global Maximum of a Convex Function: Necessary and Sufficient Conditions

نویسندگان

  • Emil Ernst
  • Michel Théra
چکیده

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

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تاریخ انتشار 2006