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Axial symmetry indices for convex cones: axiomatic formalism and applications

Alberto Seeger(alberto.seeger***at***univ-avignon.fr)
Mounir Torki(mounir.torki***at***univ-avignon.fr)

Abstract: We address the issue of measuring the degree of axial symmetry of a convex cone. By following an axiomatic approach, we introduce and explore the concept of axial symmetry index. This concept is illustrated with the help of several interesting examples. By way of application, we establish a conic version of the Blekherman inequality concerning the quality of the approximation of a convex body by its inscribed ellipsoid.

Keywords: Convex cone, axially symmetric cone, axial symmetry index, generalized reflection matrix.

Category 1: Linear, Cone and Semidefinite Programming

Citation: To appear in Journal of Convex Analysis, Vol. 26, 2019.

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Entry Submitted: 03/13/2018
Entry Accepted: 03/13/2018
Entry Last Modified: 03/13/2018

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