Practical quasi-Newton methods for solving nonlinear systems
Practical quasi-Newton methods for solving nonlinear systems
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DOI：
10.1016/s0377-0427(00)00434-9
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发表时间：
2000-12
影响因子：
2.4
通讯作者：
J. Martínez
中科院分区：
文献类型：
--
作者：
J. Martínez
研究了求解非线性系统的实用拟牛顿方法。拟牛顿方法的定义包括牛顿方法作为一种特殊情况。然而，特别强调的是每次迭代都满足割线方程的方法，这里通常称之为割线方法。重新研究了最小变化割线更新理论，并讨论了不属于最小变化割线更新族的方法的收敛结果。本文综述的方法家族包括Broyden方法、结构化准牛顿方法、直接更新分解的方法、行缩放方法和列更新方法。对一些实现特性进行了注释。调查包括对全局收敛工具和布洛登的方法的线性系统实现的讨论。在最后一节，讨论了这一领域的实践和理论观点。
Practical quasi-Newton methods for solving nonlinear systems are surveyed. The definition of quasi-Newton methods that includes Newton's method as a particular case is adopted. However, especial emphasis is given to the methods that satisfy the secant equation at every iteration, which are called here, as usually, secant methods. The least-change secant update (LCSU) theory is revisited and convergence results of methods that do not belong to the LCSU family are discussed. The family of methods reviewed in this survey includes Broyden's methods, structured quasi-Newton methods, methods with direct updates of factorizations, row-scaling methods and column-updating methods. Some implementation features are commented. The survey includes a discussion on global convergence tools and linear-system implementations of Broyden's methods. In the final section, practical and theoretical perspectives of this area are discussed.