| 一种求解非线性互补问题的filter内点算法 |
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| 引用本文： | 龙君,曾三云.一种求解非线性互补问题的filter内点算法[J].纯粹数学与应用数学,2014(3):245-254. |
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| 作者姓名： | 龙君 曾三云 |
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| 作者单位： | [1]吉首大学民族预科教育学院,湖南吉首416000 [2]吉首大学数学与统计学院,湖南吉首416000 |
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| 基金项目： | 湖南省教育厅科学研究项目（10C1126,10B088） |
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| 摘 要： | 利用Armijio条件和信赖域方法,构造新的价值函数.首次将内点算法与filter技术结合起来,提出一种求解非线性互补问题的新算法,即filter内点算法.在主算法中使用Armijio型线搜索求取步长,在修复算法中使用信赖域方法进行适当控制以保证算法的收敛性.文章还讨论了算法的全局收敛性.最后用数值实验表明了该方法是有效的.
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| 关 键 词： | 非线性互补问题 filter方法 信赖域方法 Armijio条件 全局收敛性 |
A filter interior-point algorithm for nonlinear complementarity problem |
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| Long Jun,Zeng Sanyun.A filter interior-point algorithm for nonlinear complementarity problem[J].Pure and Applied Mathematics,2014(3):245-254. |
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| Authors: | Long Jun Zeng Sanyun |
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| Institution: | 1. School of Preparatory Education for Minority Nationalities, Jishou University, Jishou 416000, China; 2. College of Mathematics and Statistics, Jishou University, Jishou 416000, China) |
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| Abstract: | A new merit function is constructed by using Armijio conditions and the trust region method. Then firstly combining the interior-point method with filter technique, we propose a new algorithm to solve nonlinear complementarity problem. In the main arithmetic, step length is produced by Armijio type line search, and in the repair algorithm, trust region method is used to properly control so as to ensure the convergence of the algorithm. We also discuss the global convergence of the algorithm. Finally, the numerical experiments show that the method is effective. |
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| Keywords: | nonlinear complementarity problem filter method trust region method Armijio conditions global convergence |
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