An Extension of a Theorem on Supports of a Convex Function

In Eisenberg, E. 1962. Supports of a convex function. Bull. Amer. Math. Soc.68 192–195, Eisenberg has given a characterization of the set of all supports of a convex function defined on a polyhedral convex cone. This extends the famous Farkas' Lemma and is very useful in programming problems. In this paper we will show that the result is true even for a larger class of convex functions.