Characterization of the Barrier Parameter of Homogeneous Convex Cones

Osman Guler and Levent Tuncel

We characterize the barrier parameter of the optimal self--concordant barriers for homogeneous cones. In particular, we prove that for homogeneous convex cones this parameter is the same as the rank of the corresponding Siegel domain and also the same as the Caratheodory number of the cone.

Research Report CORR 95-14, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, June 1995.