2:00 pm, Lecture Hall 3
New class of convex sets in semidefinite programming and their characterizations
We introduce a new class of convex set in semidefinite programming termed as 'convex set being semidefinite representable away from the origin'. It generalizes a class named 'convex set being polyhedral away from the origin', which was introduced by Victor Klee (1959). We characterize the new class and we propose new sufficient conditions for convex set to be semidefinite representable. We prove : if the set semidefinite representable away from the origin, the cone containing the convex set is semidefinite representable. Further we prove : if a convex set is semidefinite representable away from the origin, its polar is compactly semidefinite representable. Using these characterizations, we develop sufficient condition for non-compact convex set to be semidefinite representable.