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On pairs of vectors achieving the maximal angle of a convex cone

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Abstract

In this paper we explore the concept of antipodality relative to a closed convex cone . The problem under consideration is that of finding a pair of unit vectors in K achieving the maximal angle of the cone. We mention also a few words on the attainability of critical angles. By way of application of the general theory, we briefly discuss the problem of estimating the radius of pointedness of a cone.

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Authors and Affiliations

  1. Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110 - Jardim Botanico, Rio de Janeiro, Brazil

    Alfredo Iusem

  2. Department of Mathematics, University ofAvignon, 33, rue Louis Pasteur, 84000, Avignon, France

    Alberto Seeger

Authors
  1. Alfredo Iusem
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  2. Alberto Seeger
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Correspondence to Alfredo Iusem.

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Iusem, A., Seeger, A. On pairs of vectors achieving the maximal angle of a convex cone. Math. Program. 104, 501–523 (2005). https://doi.org/10.1007/s10107-005-0626-z

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  • DOI: https://doi.org/10.1007/s10107-005-0626-z

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