LOCALLY POLYHEDRAL LINEAR INEQUALITY SYSTEMS

Linear systems of an arbitrary number of inequalities provide external representations for the closed convex sets in the Euclidean space. In particular, the locally polyhedral systems introduced in this paper a re the natural linear representation for quasipolyhedral sets (those s ubsets of the Euclidean space whose nonempty intersections with polyto pes are polytopes). For these systems the geometrical properties of th e solution set are investigated, and their extreme points and edges ar e characterized. The class of locally polyhedral systems includes the quasipolyhedral systems, introduced by Marchi, Puente, and Vera de Ser io in order to generalize the Weyl property of finite linear inequalit y systems. (C) 1998 Elsevier Science Inc.