| 求不定二次规划全局解的一个新算法 |
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| 引用本文： | 黎健玲,孙小玲. 求不定二次规划全局解的一个新算法[J]. 运筹学学报, 2008, 12(3) |
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| 作者姓名： | 黎健玲 孙小玲 |
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| 作者单位： | 1. 广西大学数学与信息科学学院,南宁,530004
2. 复旦大学管理学院,上海,200433 |
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| 基金项目： | 国家自然科学基金,广西科学基金,Scientific Research Foundation of Guangxi University |
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| 摘 要： | 本文提出了一个求不定二次规划问题全局最优解的新算法.首先,给出了三种计算下界的方法:线性逼近法、凸松弛法和拉格朗日松弛法;并且证明了拉格朗日对偶界与通过凸松弛得到的下界是相等的;然后建立了基于拉格朗日对偶界和矩形两分法的分枝定界算法,并给出了初步的数值试验结果.
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| 关 键 词： | 运筹学 全局优化 不定二次规划 分枝定界方法 凸松弛 拉格朗日松弛 |
A New Algorithm for Finding Global Solution of Indefinite Quadratic Programming Problems |
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| Li Jianling,Sun Xiaoling. A New Algorithm for Finding Global Solution of Indefinite Quadratic Programming Problems[J]. OR Transactions, 2008, 12(3) |
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| Authors: | Li Jianling Sun Xiaoling |
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| Abstract: | In this paper we propose a new algorithm for finding a global solution of indefinite quadratic programming problems. We first derive three lower bounding techniques: linear approximation, convex relaxation and Lagrangian relaxation. We prove that the Lagrangian dual bound is identical to the lower bound obtained by convex relaxation. A branch-and-bound algorithm based on the Lagrangian lower bounds and rectangular bisection is then presented with preliminary computational results. |
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| Keywords: | Operations research global optimization indefinite quadratic programming branch-and-bound method convex relaxation Lagrangian relaxation |
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