Directional end of a convex set: theory and applications. (Q1608146)

The end of a nonempty convex set \(C\) in a given direction u (directional end) consists of all those points for which u is not a feasible direction with respect to \(C\). The authors discuss the properties of the directional end of general (closed) convex sets: its relation to quasipolyhedral sets and to the facial structure of \(C\), the characterizations of the extreme points and the full-dimensionality of \(C\) as well as its connection to the illumination of closed convex sets. Finally, these results are applied to the feasible set of an infinite linear inequality system.