Maximal descriptor set characterizations of efficient faces in multiple objective linear programming

In this paper we present the concept of maximal descriptor set as a way of identifying faces of a polyhedron in a unique form. This concept is based on the implicit representation of a face through its maximal set of binding inequalities. By making use of this notion it is possible to derive new practical tests to characterize the efficiency of arbitrary faces in a multiple objective linear program, some of which can be seen as extensions of other well-known results on efficiency for general points (not necessarily vertices).