facially exposed – Optimization Online

Facially dual complete (nice) cones and lexicographic tangents

Published: 2017/04/20

Convex Optimization, Linear, Cone and Semidefinite Programming boundary structure, convex cones, duality, facially dual complete, facially exposed, lexicographic tangent, tangent cone

We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the well-known and very commonly used concept of tangent cones in nonlinear … Read more

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

Published: 2002/06/10, Updated: 2002/06/18

Van Anh Truong

Levent Tunçel

Linear, Cone and Semidefinite Programming carath\'eodory number, convex optimization, facially exposed, homogeneous cones, interior point methods, self-concordant barriers, siegel domains, symmetric cones

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