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The Algebraic Structure of the p-Order Cone

Alzalg Baha (baha2math***at***gmail.com)

Abstract: We study and analyze the algebraic structure of the p-order cones. We show that, unlike popularly perceived, the p-order cone is self-dual for all p greater than or equal to 1. We establish a spectral decomposition, consider the Jordan algebra associated with this cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We generalize some important notions and properties in the Euclidean Jordan algebra of the second-order cone to the Euclidean Jordan algebra of the p-order cone.

Keywords: pth-order cones, Second-order cones, Euclidean Jordan algebras

Category 1: Linear, Cone and Semidefinite Programming

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Entry Submitted: 12/08/2015
Entry Accepted: 12/08/2015
Entry Last Modified: 01/05/2016

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