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

Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (4): 105-111.

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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.

Abstract

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

CLC Number:

O224

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

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

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