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On the symmetry of induced norm cones

Michael Orlitzky (michael***at***orlitzky.com)

Abstract: Several authors have studied the problem of making an asymmetric cone symmetric through a change of inner product, and one set of positive results pertains to the class of elliptic cones. We demonstrate that the class of elliptic cones is equal to the class of induced-norm cones that arise through Jordan-isomorphism with the second-order cone, thereby showing that this symmetry result was essentially known.

Keywords: Euclidean Jordan algebra, circular cone, elliptic cone, second-ordercone, Lorentz cone, symmetric cone

Category 1: Linear, Cone and Semidefinite Programming

Citation:

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Entry Submitted: 03/30/2020
Entry Accepted: 03/30/2020
Entry Last Modified: 06/10/2020

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