Narrowing the difficulty gap for the Celis-Dennis-Tapia problem
Seminar Room 1, Newton Institute
AbstractWe study the so-called Celis-Dennis-Tapia (CDT) problem to minimize a non-convex quadratic function over the intersection of two ellipsoids. Contrasting with the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem seems to be not yet fully understood. Our main objective in this paper is to narrow the difficulty gap defined by curvature of the Lagrangian. We propose seemingly novel sufficient and necessary conditions for local and global optimality, and hint at algorithmic possibilities to exploit these.
Key words: Copositive matrices, non-convex optimization, optimality condition, polynomial optimization, trust region problem
Co-speaker: Michael Overton, Courant Institute of Math.~Sciences, New York University, U.S.A.