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

Authors:
Alfredo Iusem;Alberto Seeger
Affiliations:
Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110 - Jardim Botanico, Rio de Janeiro, Brazil;Department of Mathematics, University ofAvignon, 33, rue Louis Pasteur, 84000, Avignon, France
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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.