Affine minorants minimizing the sum of convex functions

It is often possible to replace a convex minimization problem by an equivalent one, in which each of the original convex functions is replaced by a suitably chosen affine minorant. In this paper we identify essentially the minimal conditions permitting this replacement, and also shed light on the close and complete link between such optimal affine minorants and certain optimal dual vectors. An application to the ordinary convex programming problem is included.This research was supported in part by the National Science Foundation, Grant No. MPS75-08025, at the University of Illinois at Urbana-Champaign.