一种新的非单调修正算法Levenberg-Marquardt算法

晋慧慧, 袁柳洋, 万仲平

应用数学学报 ›› 2024, Vol. 47 ›› Issue (5) : 799-810.

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应用数学学报 ›› 2024, Vol. 47 ›› Issue (5) : 799-810. DOI: 10.20142/j.cnki.amas.202401016
论文

一种新的非单调修正算法Levenberg-Marquardt算法

    晋慧慧1, 袁柳洋1,2, 万仲平3
作者信息 +

A New Nonmonotone Modified Levenberg-marquardt Algorithm

    JIN Huihui1, YUAN Liuyang1,2, WAN Zhongping3
Author information +
文章历史 +

摘要

结合非单调线搜索技术与修正的Levenberg-Marquardt算法(L-M算法), 本文提出了一种新的求解非线性方程组的非单调修正L-M 算法. 在新算法的每次迭代中, 引入修正步, 并利用价值函数的梯度范数更新L-M参数. 如果试探步没有被接受, 则采用非单调线搜索技术来获取新的迭代点. 在一定的假设条件下, 证明了该算法的全局收敛性和局部收敛性. 数值实验结果表明, 该算法是可行和有效的.

Abstract

In this paper, a new nonmonotone modified L-M algorithm for solving nonlinear equations is proposed by combining the nonmonotone line search technique with the modified Levenberg-Marquardt algorithm (L-M algorithm). In each iteration of the new algorithm, a modified step is introduced, and the gradient norm of the value function is used to update the L-M parameters. If the trial step is not accepted, the nonmonotone line search technique is used to obtain the new iteration point. Under certain assumptions, the global convergence and local convergence of the algorithm are proved. Numerical experiment results show that the algorithm is feasible and effective.

关键词

非线性方程组 / Levenberg-Marquardt算法 / 非单调线搜索 / 收敛性

Key words

nonlinear equations / Levenberg-Marquardt algorithm / nonmonotone line search / convergence

引用本文

导出引用
晋慧慧 , 袁柳洋 , 万仲平. 一种新的非单调修正算法Levenberg-Marquardt算法. 应用数学学报, 2024, 47(5): 799-810 https://doi.org/10.20142/j.cnki.amas.202401016
JIN Huihui , YUAN Liuyang , WAN Zhongping. A New Nonmonotone Modified Levenberg-marquardt Algorithm. Acta Mathematicae Applicatae Sinica, 2024, 47(5): 799-810 https://doi.org/10.20142/j.cnki.amas.202401016
中图分类号: O221   

参考文献

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基金

国家自然科学基金(11871383,52275504);湖北省教育厅科学技术研究项目(Q20211111);湖北省冶金工业过程系统科学重点实验室开放基金项目(Y201905)资助.
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