Abstract

The focus of this talk is on two results of my recent research. The first result is the polynomial-representability of homogeneous cones by positive definite cone. Using $T$-algebras, a class of non-associative algebras invented by Vinberg in the early 1960's, I proved that each homogeneous cone can be expressed as the intersection of a cone of positive definite matrices and a linear subspace. This immediately implies that a homogeneous cone programming can be modeled as a semi-definite programming problem. The second result is a new primal-dual algorithm for semi-definite programming. By using second-order cone approximations to positive cone, I developed a new primal-dual interior-point algorithm for semi-definite programming that runs in $O(\sqrt{n})$ iterations, the best bound known.

FRIDAY, February 28, 2003
Time: 4:30 P.M.
Location: WeH 7500