Recent progress in the global convergence of quasi-Newton methods for nonlinear equations
Recent progress in the global convergence of quasi-Newton methods for nonlinear equations
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DOI：
10.14492/hokmj/1272848030
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发表时间：
2007-11
影响因子：
0.5
通讯作者：
Donghui Li;W. Cheng
中科院分区：
文献类型：
--
作者：
Donghui Li;W. Cheng
关于最优化问题的拟牛顿方法的全局收敛理论已经被很好地建立起来。与非线性方程组拟牛顿方法的全球化相关的工作相对较少。非线性方程组拟牛顿方法全球化的主要困难在于缺乏有效的线搜索技术。最近，又有人提出了一些免导数的行搜索。一些拟牛顿算法在全局收敛方面的研究取得了很好的进展。本文综述了求解非线性方程的拟牛顿方法在全局收敛方面的一些最新进展。
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, then 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.