On existence and uniqueness of a vector minimizing a convex function

Abstract

In this paper, theorems on existence and uniqueness of a vector minimizing a closed proper convex functionf are given, extending previous results on this topic. Necessary and sufficient conditions are presented for convex functions with additional properties. Iff attains its infimum atx withoutx being unique, linear functionsd'x with unique or bounded values are identified. Applicability of results is demonstrated in regression analysis of failure times, including the Cox model.