分野別セミナー

Semidefinite program (SDP) is the convex minimization on matrix variables. Some efficient algorithms to solve SDPs, e.g., the ellipsoid method and interior-point method are proposed, and applications of combinatorial optimization, polynomial optimization, control and statistics etc are well-known. The strict feasibility of SDP guarantees the celebrated strong duality theorem on SDP and the convergence of algorithms to solve SDP. However non-strictly feasible SDPs often appear in these applications, and the numerical behavior of algorithms for SDPs are numerically unstable. We talk about computational aspects on such SDPs. In particular, we show that in some of the applications, the non-strict feasibility comes from an intrinsic nature of the applications.