Preprint A375/2005
Computing the radius of pointedness of a convex cone

Alberto Seeger | Iusem, Alfredo N.

**Keywords: **
convex cones | pointedness

Consider the space of closed and convex cones in a finite dimensional space, with the Hausdorff-Pompei metric. The set of pointed cones is open in this metric space, and we can measure the degree of pointedness of a cone K with the distance from K to the set of non-pointed coes. This distance is called radius of pointedness of K.In this paper we give a simple formula for the radius of pointedness of any cone whose maximal angle does not exceed 120 degrees. For these cones, we also construct explicitly
the non-pointed cone which lies at minimal distance to the given pointed cone.