September 19, 2008:

Olena Shevchenko, WMU

Classification of Homogeneous Convex Cones, T-algebras, and Interior-Point Methods for Convex Optimization



Abstract.  

A cone K is called homogeneous if for any two points x and y in K there exists a non-degenerate linear automorphism A of K (i.e. AK=K) such that Ax=y. Homogeneous cones were partially classified in terms of T-algebras by Vinberg. He proved that each homogeneous cone is isomorphic to a cone of generalized positive-definite Hermitian matrices. In the talk, we will present key results that lead to this classification, introduce T-algebras, and talk about applications in the interior-point theory for convex programming problems.