Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set

摘要

This article presents new conditions that ensure the closedness of a convex cone in terms of the end set and the extent of its generator. The results significantly extend the classic condition. The new closedness conditions are utilized to obtain a simple formula of the least global error bound and a suitable regularity condition of the set containment problem for sublinear functions.