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
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.
|Uncontrolled Keywords||Nonlinear equation, quasi-Newton method, derivative-free line search, global convergence|