Facial exposedness

Classification of facial exposedness of completely positive cones over symmetric cones

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

We classify the facial exposedness of completely positive cones over symmetric cones in terms of the rank of the associated Euclidean Jordan algebras. The completely positive cones are facially exposed when the rank is at most $2$, but are not facially exposed when the rank is at least $5$. Facial exposedness is not completely determined … Read more

Non-facial exposedness of copositive cones over symmetric cones

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , ,

In this paper, we consider copositive cones over symmetric cones and show that they are never facially exposed when the underlying cone has dimension at least 2. We do so by explicitly exhibiting a non-exposed extreme ray. Our result extends the known fact that the cone of copositive matrices over the nonnegative orthant is not … Read more