Goldstein线搜索下Levenberg-Marquardt方法的全局收敛性

运筹学学报 ›› 2012, Vol. 16 ›› Issue (4): 105-111.

Goldstein线搜索下Levenberg-Marquardt方法的全局收敛性

杜守强¹

1. 青岛大学数学科学学院

出版日期:2012-12-15 发布日期:2012-12-15
通讯作者: 杜守强 E-mail:dsq8933@163.com

Global convergence of the Levenberg-Marquardt method with Goldstein line search

DU Shouqiang¹

1. College of Mathematics, Qingdao University

Online:2012-12-15 Published:2012-12-15
Contact: DU Shouqiang E-mail:dsq8933@163.com
Supported by:
Supported by National Natural Science Fundation of China (Nos. 11101231, 10971118), Shandong Province Higher Educational Science and Technology Program (No. J10LA05), International Cooperation Program for Excellent Lecturers of 2011 by Shandong Provincial Education Department.

摘要/Abstract

摘要： 给出在Goldstein线搜索条件下求解非线性方程的Levenberg-Marquardt方法, 在较为温和的条件下证明了该方法的全局收敛性, 并且利用该方法对广义互补问题进行了求解分析.

关键词: 全局收敛, Levenberg-Marquardt方法, 线搜索, 非线性方程

Abstract: In this paper, we consider the Levenberg-Marquardt method for solving nonlinear equations. We use Goldstein line search on every iteration to guarantee the global convergence of the Levenberg-Marquardt method. Under mild conditions, we prove that the Levenberg-Marquardt method is globally convergent. And we also apply the method to solve generalized complementarity problems.

Key words: global convergence, Levenberg-Marquardt method, line search, nonlinear equations

中图分类号:

O224

杜守强. Goldstein线搜索下Levenberg-Marquardt方法的全局收敛性[J]. 运筹学学报, 2012, 16(4): 105-111.

DU Shouqiang. Global convergence of the Levenberg-Marquardt method with Goldstein line search[J]. Operations Research Transactions, 2012, 16(4): 105-111.

参考文献

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