Characterizations of efficient solutions under polyhedrality assumptions

Abstract

We give severa! characterizations of efficient solutions of subsets of RP (with respect to compatible preorders) in terms of the lexicographical order, under the assumptions that the set of admissible points is a convex polyhedron or the nonnegative cone corresponding to the preorder is polyhedral. We also characterize the lexicographical minimum of a convex polyhedron by means of the componentwise order and unitary lower triangular matrices.