Antipoldality in convex cones and distance to unpointedness
Alberto Seeger | Iusem, Alfredo
Convex cone | antipodality | distance to unpointedness
We provide a complete answer to the problem consisting of finding an unpointed closed convex cone lying at minimal bounded Pompeiu-Hausdorff distance to a pointed one. We give also a simple and useful characterization of the radius of pointedness of a convex cone. A corresponding characterization of the radius of solidity is then derived by using a duality argument.