Preprint A232/2003
Measuring the degree of pointedness of a closed convex cone: a metric approach

Alberto Seeger | Iusem, Alfredo N.

**Keywords: **
pointed cone | solid cone | radius of pointedness | polarity | elliptic cone

We introduce the concept of radius of pointedness for a closed cone in a finite dimensional Hilbert space, which measures the degree of pointedness of the cone: the bigger the radius, the higher its degree of pointedness. We also discuss the issue of measuring the degree of solidity of a closed convex cone. Pointedness and solidity radiuses are related to each other through a simple duality formula. Explicit conputations are carried out for several classical cones appearing in the literature.