网站原创收稿日期:2009-11-30.
基金项目:国家自然科学基金（10771162）.
作者简介:黎维清（1987-）,男,硕士研究生.主要研究方向：运筹学.
通讯作者：濮定国（1948-）,男,教授,博士生导师.主要研究方向：运筹学.
摘 要 : 提出了一个新的求解非线性方程组的滤子算法,首先把非线性方程组的求解转化成一个非线性优化问题,然后借助非单调技术和滤子技术求解该问题,从而得到了原方程组的解.在适当的条件下,证明了该算法的全局收敛性,初步的数值试验表明了该算法的有效性.
关 键 词 : 非线性方程组；滤子；非单调技术；全局收敛性
中图分类号:O221.2
文献标识码:A文章编号:1672-8513(2010)04-0253-04
A Nonmonotone Filter Method for Nonlinear Equations
LI Weiqing,PU Dingguo
（Department of Mathematics,Tongji University,Shanghai 200092, China）
Abstract: This paper presents a new filter method for solving nonlinear equations. First,this problem is tranormed into a nonlinear optimization. Then, it solves this question with the aid of nonmonotone technology and filter technology,and thus obtains a solution of the original nonlinear equation. Under reasonable conditions,it shows the global convergence properties. Preliminary numerical tests he proved the efficiency of the approach.
Key words: nonlinear equations, filter, nonmonotone technology, global convergence