Global Optimality Conditions for Quadratic Program Problems with Quadratic Constraints

In this paper, sufficient global optimality conditions are presented for nonconvex quadratic programming problems with quadratic constraints as well as hyperrectangle constraints. The new conditions are obtained by making use of quadratic underestimators of quadratic function. We first introduce how to construct quadratic underestimators of quadratic function.Then, by using convex quadratic underestimators of the Lagrangian function at the KarushKuhn-Tucker point, we establish sufficient global optimality conditions for nonconvex quadratic programming problems. And we propose sufficient global optimality conditions by utilizing the minimum eigenvalue and quadratic underestimators. Finally, by using quadratic underestimators, we establish the sufficient condition for nonconvex quadratic programming problems with quadratic constraints.