Selected Applications of Linear Semi-Infinite Systems Theory

Abstract

In this paper we, …rstly, review the main known results on systems of an arbitrary (possibly in…nite) number of weak linear inequalities posed in the Euclidean space R n (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two signi…cant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdi¤erentials, recovering known results in both …elds and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of in…nite sets of sites by appealing to well-known results on linear semi-in…nite systems.