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Relating homogeneous cones and positive definite cones via T-algebras.

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Relating homogeneous cones and positive definite cones via T-algebras.

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Title: Relating homogeneous cones and positive definite cones via T-algebras.
Author: Chua, Chek Beng.
Copyright year: 2003
Abstract: T-algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone K(A) for each T-algebra A and proved that every homogeneous cone is isomorphic to one such K(A). We relate each T-algebra A with a space of linear operators in such a way that K(A) is isomorphic to the cone of positive definite self-adjoint operators. Together with Vinberg’s result, we conclude that every homogeneous cone is isomorphic to a “slice” of a cone of positive definite matrices.
Subject: DRNTU::Science::Mathematics::Applied mathematics::Optimization.
Type: Journal Article
Series/ Journal Title: SIAM Journal on Optimization.
School: School of Physical and Mathematical Sciences
Rights: SIAM Journal on Optimization @ copyright 2003 The journal's website is located at http://www.siam.org/journals/siopt.php.
Version: Published version

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