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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (1): 21-28.doi: 10.3969/j.issn.1005-3085.2015.01.003

• • 上一篇    下一篇

具有二次约束的二次规划全局最优性条件

周雪刚1,2   

  1. 1- 广东金融学院应用数学系，广州 510521
    2- 广州大学数学与信息科学学院，广州 510006
  • 收稿日期:2013-09-09 接受日期:2014-07-28 出版日期:2015-02-15 发布日期:2015-04-15
  • 基金资助:
    中国博士后科学基金 (2014M562152)；广东省自然科学基金博士科研启动基金 (S2013040012506).

Global Optimality Conditions for Quadratic Program Problems with Quadratic Constraints

ZHOU Xue-gang1,2   

  1. 1- Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521
    2- School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
  • Received:2013-09-09 Accepted:2014-07-28 Online:2015-02-15 Published:2015-04-15
  • Supported by:
    The Postdoctoral Science Foundation Funded of China (2014M562152); the Ph.D. Start-up Fund of Natural Science Foundation of Guangdong Province (S2013040012506).

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摘要： 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．

关键词: 非凸二次规划, 全局最优性条件, 二次下估计函数

Abstract:

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 underestimators, we establish the sufficient condition for nonconvex quadratic programming problems with quadratic constraints.

Key words: nonconvex quadratic program, global optimality conditions, quadratic underestimators

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