基于Armijo非单调线搜索的修正LM方法
A Modified Levenberg-Marquardt Method with an Armijo Nonmonotone Line Search
DOI: 10.12677/AAM.2022.119689, PDF,   
作者: 陈 咪：长沙理工大学数学与统计学院，湖南 长沙
关键词: 非线性方程组；LM方法；非单调线搜索；全局收敛；Nonlinear Equations； LM Method； Nonmonotone Line Search； Global Convergence
摘要: 近年来，非线性方程组问题越来越多地出现在科学与工程领域中。Levenberg-Marquardt (LM)方法是解决此问题的有效方法。为了避免信赖域步不可取的情况，文章提出一种基于非单调线搜索技术的修正LM方法，同样保证了算法在局部误差界的条件下达到全局收敛，并在文末附上了相应的数值结果，证明算法是有效的。
Abstract: Recently, systems of nonlinear equations have wide application in fields of science and engineering. The Levenberg-Marquardt method is an effective method to solve this problem. In this paper, we propose a modified Levenberg-Marquardt method by using a nonmonotone line search technique for the nonlinear equations system to avoid the situation where a trust step is not acceptable. The global and cubic convergence of this new method is also preserved under the local error bound con-dition. Finally, some numerical results are reported, which show that the algorithm is efficient.
文章引用：陈咪. 基于Armijo非单调线搜索的修正LM方法[J]. 应用数学进展, 2022, 11(9): 6511-6520. https://doi.org/10.12677/AAM.2022.119689

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