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Chek Beng Chua (cbchuamath.uwaterloo.ca) Abstract: $T$algebras are nonassociative algebras defined by Vinberg in the early 1960's for the purpose of studying homogeneous cones. Vinberg defined a cone $K(\mathcal A)$ for each $T$algebra $\mathcal A$ and proved that every homogeneous cone is isomorphic to one such $K(\mathcal A)$. We relate each $T$algebra $\mathcal A$ with a space of linear operators in such a way that $K(\mathcal A)$ is isomorphic to the cone of positive definite selfadjoint operators. Together with Vinberg's result, we conclude that every homogeneous cone is isomorphic to a ``slice'' of a cone of positive definite matrices. Keywords: homogeneous cones, Talgebras, semidefinite programming, interiorpoint methods Category 1: Linear, Cone and Semidefinite Programming (Other ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: SIAM J. Optim., 2003, 14:500506 Download: Entry Submitted: 05/06/2002 Modify/Update this entry  
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