Nonnegative generalized inverses and least elements of polyhedral sets

In this article, a classical result of Cottle and Veinott characterizing least elements of polyhedral sets in terms of nonnegative left-inverses is extended to characterize nonnegativity of some of the most important generalized inverses. We also present generalizations of the other results of these authors for the case of the Moore-Penrose inverse. © 2011 Published by Elsevier Inc.