Preprint A550/2007
Antipoldality in convex cones and distance to unpointedness

Alberto Seeger | Iusem, Alfredo

**Keywords: **
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.