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 are the natural linear representation for quasipolyhedral sets (those subsets of the Euclidean space whose nonempty intersections with polytopes are polytopes). For these systems the geometrical properties of the solution set are investigated, and their extreme points and edges are characterized. The class of locally polyhedral systems includes the quasipolyhedral systems, introduced by Marchi, Puente, and Vera de Serio in order to generalize the Weyl property of finite linear inequality systems.