求解非线性方程组的非单调自适应加速Levenberg-Marquardt算法

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (3): 538-546.

求解非线性方程组的非单调自适应加速Levenberg-Marquardt算法

曹名圆¹, 李蓉¹, 闫雪丽¹, 黄庆道²

1. 北华大学数学与统计学院, 吉林吉林 132013; 2. 吉林大学数学学院, 长春 130012

收稿日期:2023-08-20 出版日期:2024-05-26 发布日期:2024-05-26
通讯作者: 黄庆道 E-mail:huangqd@jlu.edu.cn

Nonmonotonic Adaptive Accelerated Levenberg-Marquardt Algorithm for Solving Nonlinear Equations

CAO Mingyuan¹, LI Rong¹, YAN Xueli¹, HUANG Qingdao²

1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;
2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2023-08-20 Online:2024-05-26 Published:2024-05-26

摘要/Abstract

摘要： 提出一种新的求解非线性方程组的非单调自适应加速Levenberg-Marquardt算法, 该算法使用一种新的自适应函数更新Levenberg-Marquardt参数, 这种Levenberg-Marquardt参数的更新方式可提高过于成功的迭代中模型与目标函数的一致性, 从而加快算法的收敛速度. 数值实验结果表明, 该算法具有良好的数值计算性能.

关键词: 自适应函数, 非单调技术, 加速Levenberg-Marquardt算法

Abstract: We proposed a new nonmonotonic adaptive accelerated Levenberg-Marquardt algorithm for solving nonlinear equations. The algorithm used a new adaptive function to update the Levenberg-Marquardt parameter, which could enhance the consistency between the model and objective function during too-successful iterations, thereby accelerating the convergence rate of the algorithm. Numerical experimental results show that the proposed algorithm has good numerical computational performance.

Key words: adaptive function, nonmonotonic technique, accelerated Levenberg-Marquardt algorithm

中图分类号:

O221.2

曹名圆, 李蓉, 闫雪丽, 黄庆道. 求解非线性方程组的非单调自适应加速Levenberg-Marquardt算法[J]. 吉林大学学报(理学版), 2024, 62(3): 538-546.

CAO Mingyuan, LI Rong, YAN Xueli, HUANG Qingdao. Nonmonotonic Adaptive Accelerated Levenberg-Marquardt Algorithm for Solving Nonlinear Equations[J]. Journal of Jilin University Science Edition, 2024, 62(3): 538-546.