Convex functions on convex polytopes
Authors: David Gale, Victor Klee and R. T. Rockafellar
Journal: Proc. Amer. Math. Soc. 19 (1968), 867-873
MSC: Primary 52.10; Secondary 90.00
MathSciNet review: 0230219
Abstract: The behavior of convex functions is of interest in connection with a wide variety of optimization problems. It is shown here that this behavior is especially simple, in certain respects, when the domain is a polytope or belongs to certain classes of sets closely related to polytopes; moreover, the polytopes and related classes are actually characterized by this simplicity of behavior.
The following corollary is useful in mathematical economics: If is a boundedly polyhedral set and is a convex function on the relative interior of such that is bounded on bounded sets, then can be extended in a unique way to a continuous convex function on .
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