The Algebraic Structure of the Arbitrary-Order Cone

Baha Alzalg ()
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Baha Alzalg: The University of Jordan

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 1, No 3, 32-49

Abstract: 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 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0878-1

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