Antipodality in convex cones and distance to unpointedness

We provide a complete answer to the problem which consists in finding an unpointed convex cone lying at minimal bounded Pompeiu-Hausdorff distance from a pointed one. We give also a simple and useful characterization of the radius of pointedness of a convex cone. A corresponding characterization for the radius of solidity of a convex cone is then derived by using a duality argument.

• Type: Journal
• Year: 2008
• Where: APPML
• Authors: Alfredo N. Iusem, Alberto Seeger
• Keywords: APPML 2008, Complete Answer, Convex Cone, Unpointed Convex Cone