Hokkaido Mathematical Journal

Recent progress in the global convergence of quasi-Newton methods for nonlinear equations

Dong-Hui LI and Wanyou CHENG

Full-text: Open access

Abstract

The global convergence theory of quasi-Newton methods for optimization problems has well been established. Related work to the globalization of quasi-Newton methods for nonlinear equations is relatively less. The major difficulty in globalizing quasi-Newton methods for nonlinear equations lies in the lack of efficient line search technique. Recently, there have been proposed some derivative-free line searches. The study in the global convergence of some quasi-Newton methods has taken good progress. In this paper, we summarize some recent progress in the global convergence of quasi- Newton methods for solving nonlinear equations.

Article information

Source
Hokkaido Math. J., Volume 36, Number 4 (2007), 729-743.

Dates
First available in Project Euclid: 3 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1272848030

Digital Object Identifier
doi:10.14492/hokmj/1272848030

Mathematical Reviews number (MathSciNet)
MR2378288

Zentralblatt MATH identifier
1138.65039

Subjects
Primary: 90C53: Methods of quasi-Newton type
Secondary: 65H10: Systems of equations

Keywords
Nonlinear equation quasi-Newton method derivative-free line search global convergence

Citation

LI, Dong-Hui; CHENG, Wanyou. Recent progress in the global convergence of quasi-Newton methods for nonlinear equations. Hokkaido Math. J. 36 (2007), no. 4, 729--743. doi:10.14492/hokmj/1272848030. https://projecteuclid.org/euclid.hokmj/1272848030


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