| 一种求解非线性互补问题的外梯度-Filter方法 |
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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外梯度-Filter方法[J]. 吉首大学学报(自然科学版), 2014, 35(4): 19-22. DOI: 10.3969/j.issn.1007-2985.2014.04.005 |
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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： | 结合 Josephy-Newton方法，建立了一种不含价值函数的求解非线性互补问题的全局策略.该策略基于外梯度步和Filter技术，提出一个外梯度-Filter算法.此算法中的外梯度步可以减少与最优解之间的距离，从而使该算法具有全局收敛性.在适当的条件下，该算法还具有超线性收敛性.
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| 关 键 词： | 非线性互补问题 Filter技术 Josephy-Newton方法 外梯度步 收敛性 |
Extragradient-Filter Method for Solving Nonlinear Complementarity Problems |
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| LONG Jun,ZENG San-Yun. Extragradient-Filter Method for Solving Nonlinear Complementarity Problems[J]. Journal of Jishou University(Natural Science Edition), 2014, 35(4): 19-22. DOI: 10.3969/j.issn.1007-2985.2014.04.005 |
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| Authors: | LONG Jun ZENG San-Yun |
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| Affiliation: | (1.School of Preparatory Education for Minority Nationalities，Jishou University,Jishou 416000,Hunan China;2.College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China) |
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| Abstract: | Combined with the Josephy-Newton method, a new globalization strategy without any merit function was established for nonlinear complementarity problem. The strategy presents an extragradientfilter algorithm based on extragradient step and filter technology. The extragradient step can reduce the distance with the optimal solution of the problem. So the resulting algorithm is globally convergent to a solution. Under natural assumptions,locally superlinear rate of convergence can be obtained. |
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| Keywords: | nonlinear complementarity problem filter technology Josephy-Newton method extragradient step convergence |
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