一种求解非线性互补问题的外梯度-Filter方法

doi:10.3969/j.issn.1007-2985.2014.04.005

journal6 ›› 2014, Vol. 35 ›› Issue (4): 19-22.DOI: 10.3969/j.issn.1007-2985.2014.04.005

一种求解非线性互补问题的外梯度-Filter方法

龙君,曾三云

(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)

出版日期:2014-07-25 发布日期:2014-07-21
作者简介:龙君(1973- )，男，湖南凤凰人，吉首大学民族预科教育学院讲师，博士生，主要从事基于Filter方法的理论与算法研究.
基金资助:
湖南省教育厅科学研究项目（10C1126，10B088）

Extragradient-Filter Method for Solving Nonlinear Complementarity Problems

LONG Jun, ZENG San-Yun

(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)

Online:2014-07-25 Published:2014-07-21

摘要/Abstract

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.

关键词： 非线性互补问题, Filter技术, Josephy-Newton方法, 外梯度步, 收敛性

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 extragradient-filter 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.

Key words: nonlinear complementarity problem, filter technology, Josephy-Newton method, extragradient step, convergence

龙君, 曾三云. 一种求解非线性互补问题的外梯度-Filter方法[J]. journal6, 2014, 35(4): 19-22.

LONG Jun, ZENG San-Yun. Extragradient-Filter Method for Solving Nonlinear Complementarity Problems[J]. journal6, 2014, 35(4): 19-22.

参考文献

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[11] LONG Jun,MA Changfeng,NIE Puyan.A New Filter Method for Solving Nonlinear Complementarity Problems[J].Applied Mathematics and Computation,2007(185):705-718.

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[14] LONG Jun,ZENG Sanyun.A New Filter-Levenberg-Marquardt Method with Disturbance for Solving Nonlinear Complementarity Problems[J].Applied Mathematics and Computation,2010,216(2):677-688.

一种求解非线性互补问题的外梯度-Filter方法

Extragradient-Filter Method for Solving Nonlinear Complementarity Problems

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