The Algebraic Structure of the Arbitrary-Order Cone

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Abstract

We study and analyze the algebraic structure of the arbitrary-order cones. We show that, unlike popularly perceived, the arbitrary-order cone is self-dual for any order 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 arbitrary-order cone.

Keywords

pth-order cones Second-order cones Euclidean Jordan algebras 
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Notes

Acknowledgments

The author thanks the anonymous referees for their valuable suggestions to improve the paper.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceThe University of JordanAmmanJordan

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