- Relating Homogeneous Cones and Positive Definite Cones via $T$-algebras Chek Beng Chua (cbchuamath.uwaterloo.ca) Abstract: $T$-algebras are non-associative 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 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. Keywords: homogeneous cones, T-algebras, semidefinite programming, interior-point methods Category 1: Linear, Cone and Semidefinite Programming (Other ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: SIAM J. Optim., 2003, 14:500-506 Download: Entry Submitted: 05/06/2002Entry Accepted: 05/07/2002Entry Last Modified: 03/29/2004Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.