We establish a geometric condition guaranteeing exact copositive relaxationfor the nonconvex quadratic optimization problem under two quadratic andseveral linear constraints, and present sufficient conditions for globaloptimality in terms of generalized Karush-Kuhn-Tucker multipliers. Thecopositive relaxation is tighter than the usual Lagrangian relaxation. Weillustrate this by providing a whole class of quadratic optimization problemsthat enjoys exactness of copositive relaxation while the usual Lagrangianduality gap is infinite. Finally, we also provide verifiable conditions underwhich both the usual Lagrangian relaxation and the copositive relaxation areexact for an extended CDT (two-ball trust-region) problem. Importantly, thesufficient conditions can be verified by solving linear optimization problems.
展开▼
