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

✍ Scribed by Alfredo Iusem; Alberto Seeger

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
219 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

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. (Β© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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