Hokkaido Mathematical Journal

LI Dong-Hui, CHENG Wanyou,

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

Hokkaido Mathematical Journal, 36 (2007) pp.729-743

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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.

MSC(Primary)90C53
MSC(Secondary)65H10
Uncontrolled KeywordsNonlinear equation, quasi-Newton method, derivative-free line search, global convergence