| 线性互补问题与多目标优化 |
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| 引用本文： | 雍龙泉,刘三阳,邓方安,张建科,杨国平.线性互补问题与多目标优化[J].数学杂志,2014,34(3):546-552. |
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| 作者姓名： | 雍龙泉 刘三阳 邓方安 张建科 杨国平 |
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| 作者单位： | 陕西理工学院数学与计算机科学学院;西安电子科技大学理学院;西安邮电大学理学院; |
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| 基金项目： | 国家自然科学基金资助(60974082);陕西省教育厅科研计划项目(12JK0863);西安电子科技大学研究生创新基金项目(K50513100004) |
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| 摘 要： | 本文研究了求解线性互补问题的一类新方法:把线性互补问题转化为多目标优化问题,利用多目标优化有效解的定义,给出了零有效解的概念;进而获得多目标优化问题的零有效解就是线性互补问题的最优解.最后给出了有解、无解线性互补问题,并分别把这些问题转化为多目标优化,采用极大极小方法求解转化后的多目标优化问题.数值实验结果表明了该方法的正确性和有效性,完善了文献19]的数值结果.
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| 关 键 词： | 线性互补问题 多目标优化问题 极大极小方法 |
| 收稿时间： | 2013/1/24 0:00:00 |
| 修稿时间： | 2013/4/17 0:00:00 |
LINEAR COMPLEMENTARITY PROBLEM ANDMULTIOBJECTIVE OPTIMIZATION |
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| YONG Long-quan,LIU San-yang,DENG Fang-an,ZHANG Jian-ke and YANG Guo-ping.LINEAR COMPLEMENTARITY PROBLEM ANDMULTIOBJECTIVE OPTIMIZATION[J].Journal of Mathematics,2014,34(3):546-552. |
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| Authors: | YONG Long-quan LIU San-yang DENG Fang-an ZHANG Jian-ke and YANG Guo-ping |
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| Institution: | School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China,School of Science, Xidian University, Xi''an 710071, China,School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China,School of Science, Xi''an University of Posts and Telecommunications, Xi''an 710121, China and School of Science, Xidian University, Xi''an 710071, China |
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| Abstract: | A new method is proposed for the linear complementarity problem (LCP). First we reduce the LCP into a multiobjective optimization problem (MOP), and we deflne zero-efficient solution based on the efficient solution to MOP. Then we indicate that zero-efficient solution to the MOP is also the solution to the LCP. Finally some solvable and unsolvable LCP examples are transformed respectively into MOP and solved by minimax method. Numerical results indicate that the proposed method is efiective, which improved numerical results in 19]. |
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| Keywords: | linear complementarity problem multiobjective optimization problem minimax method |
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