具有二次约束的二次规划全局最优性条件∗

摘要

In this paper, sufficient global optimality conditions are presented for nonconvex quadratic programming problems with quadratic constraints as well as hyperrectangle constr-aints. 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 Karush-Kuhn-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 underestima-tors, we establish the sufficient condition for nonconvex quadratic programming problems with quadratic constraints.%本文讨论具有二次约束与超矩形约束的非凸二次规划问题的新型全局最优性充分条件，这些新的全局最优性充分条件是利用二次函数的二次下估计函数获得的。我们首先介绍如何构造二次函数的下估计函数。然后利用在KKT点处的拉格朗日函数的凸二次下估计函数建立非凸二次规划问题的全局最优性充分条件，再利用最小特征根与二次下估计函数获得它的全局最优性充分条件。最后利用二次下估计函数建立具有二次约束的非凸二次规划问题的全局最优性充分条件。