Measuring the degree of pointedness of a closed convex cone: a metric approach

Abstract We introduce the concept of radius of pointedness for a closed convex cone in a finite dimensional Hilbert space. Such radius measures the degree of pointedness of the cone: the bigger the radius, the higher its degree of pointedness. We also discuss the question 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 computations are carried out for several classical cones appearing in the literature. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)