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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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dc.contributor.author Chua, Chek Beng.
dc.date.accessioned 2009-07-27T07:19:12Z
dc.date.available 2009-07-27T07:19:12Z
dc.date.copyright 2003
dc.date.issued 2009-07-27T07:19:12Z
dc.identifier.citation Chua, C. B., (2003). Relating homogeneous cones and positive definite cones via T-algebras. SIAM Journal on Optimization, 14(2), 500-506.
dc.identifier.issn 1095-7189
dc.identifier.uri http://hdl.handle.net/10220/4702
dc.description.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.
dc.format.extent 7 p.
dc.language.iso en
dc.relation.ispartofseries SIAM Journal on Optimization.
dc.rights SIAM Journal on Optimization @ copyright 2003 The journal's website is located at http://www.siam.org/journals/siopt.php.
dc.subject DRNTU::Science::Mathematics::Applied mathematics::Optimization.
dc.title Relating homogeneous cones and positive definite cones via T-algebras.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.doi http://dx.doi.org/10.1137/S1052623402406765
dc.description.version Published version

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