| 求解带二次约束的非凸二次规划的一种分支定界算法 |
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| 引用本文： | 杨永健,高岳林.求解带二次约束的非凸二次规划的一种分支定界算法[J].应用数学,2006,19(1):25-29. |
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| 作者姓名： | 杨永健 高岳林 |
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| 作者单位： | 1. 上海大学数学系,上海,200444
2. 上海大学数学系,上海,200444;西北第二民族学院信息与计算科学系,宁夏,银川,750021 |
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| 摘 要： | 本文提出了一种求解带二次约束和线性约束的二次规划的分支定界算法.在算法中,我们运用Lipschitz条件来确定目标函数和约束函数的在每个n矩形上的上下界,对于n矩形的分割,我们采用选择n矩形最长边的二分法,同时我们采用了一些矩形删除技术,在不大幅增加计算量的前提下,起到了加速算法收敛的效果.从理论上我们证明了算法的收敛性,同时数值实验表明该算法是有效的.
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| 关 键 词： | 二次规划 二次约束 分支定界 最优化 |
| 文章编号： | 1001-9847(2006)01-0025-05 |
| 收稿时间： | 2004-09-03 |
| 修稿时间： | 2004年9月3日 |
A Branch and Bound Algorithm for Nonconvex Quadratic Programming with Quadratic Constraints |
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| YANG Yong-jian,GAO Yue-lin.A Branch and Bound Algorithm for Nonconvex Quadratic Programming with Quadratic Constraints[J].Mathematica Applicata,2006,19(1):25-29. |
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| Authors: | YANG Yong-jian GAO Yue-lin |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai 200444, China ; 2. Department of Informational and Computational Science, Northwest Secondly National College, Yinchuan 750021, China |
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| Abstract: | In this paper a branch and bound approach for nonconvex quadratic programming with quadratic constrained is introduced.In the proposed algorithm,we make use of the Lipschitz condition to determine lower bounds of functions over each rectangle.Further,convergence of the algorithm is proved.The implementation of the algorithms on several test problems is reported with satisfactory numerical results. |
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| Keywords: | Quadratic programming Branch and bound algorithm Lipschitz condition |
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