Narrowing the difficulty gap for the CelisDennisTapia problem
We study the CelisDennisTapia (CDT) problem: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that occurs when the Hessian of the Lagrangian is indefinite at all KarushKuhnTucker points. We prove new sufficient and necessary conditions both for local and global optimality, based on copositivity, giving a complete characterization in the degenerate case.
trust region problem copositive matrices non-convex optimization global optimality condition polynomial optimization 90c20 90c26