On the Existence of Solutions for Linear Inequality Systems

A system of an arbitrary number of linear inequalities, over a real locally convex space, is called either consistent or asymptotically consistent depending on the existence of ordinary solutions or weak solutions, respectively. When such a system has no weak solution, it will be called strongly inconsistent. In this paper different criteria for the classification of a given system are provided. Some of these criteria are based upon the properties of certain wedges associated with the system, and their close relations with the concept of ascent ray are emphasized. The classification criteria provided in this paper apply to the structural analysis of the main models in (semi-)infinite linear programming.