Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers

We study homogeneous convex cones. We first characterize the extreme rays of such cones in the context of their primal construction (due to Vinberg) and also in the context of their dual construction (due to Rothaus). Then, using these results, we prove that every homogeneous cone is facially exposed. We provide an alternative proof of … Read more