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Measuring axial symmetry in convex cones

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

Abstract: The problem of measuring the degree of central symmetry of a convex body has been treated by various authors since the early twentieth century. This work addresses the issue of measuring the degree of axial symmetry of a convex cone. Passing from central symmetry in convex bodies to axial symmetry in convex cones is not a mere routine. Although it is possible to push the parallelism between both issues at a great level of generality, there are a number of substantial differences as well.

Keywords: Convex cone, axially symmetric cone, axial symmetry degree, generalized reflection matrices.

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization

Citation: To appear in Journal of Convex Analysis (accepted in June 2017).

Download: [PDF]

Entry Submitted: 07/20/2017
Entry Accepted: 07/20/2017
Entry Last Modified: 07/20/2017

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