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

Iusem Alfredo | Zendy; Seeger Alberto | Zendy

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

Author(s) -

Iusem Alfredo,

Seeger Alberto

Publication year - 2006

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310380

Subject(s) - dual cone and polar cone , solidity , mathematics , cone (formal languages) , degree (music) , convex cone , radius , regular polygon , duality (order theory) , metric (unit) , hilbert space , simple (philosophy) , space (punctuation) , mathematical analysis , pure mathematics , geometry , subderivative , convex optimization , physics , computer science , algorithm , philosophy , operations management , computer security , epistemology , acoustics , economics , programming language , operating system

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)

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