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

Nonmonotonic Adaptive Accelerated Levenberg-Marquardt Algorithm for Solving Nonlinear Equations

作　　者：曹名圆[1] 李蓉 闫雪丽 黄庆道[2] CAO Mingyuan;LI Rong;YAN Xueli;HUANG Qingdao(School of Mathematics and Statistics,Beihua University,Jilin 132013,Jilin Province,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[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

出　　处：《吉林大学学报（理学版）》2024年第3期538-546,共9页Journal of Jilin University:Science Edition

基　　金：吉林省自然科学基金重点项目(批准号:YDZJ202101ZYTS167,YDZJ202201ZYTS303);北华大学研究生创新项目(批准号:2022033).

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.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.

关 键 词：自适应函数 非单调技术 加速Levenberg-Marquardt算法 

分 类 号：O221.2[理学—运筹学与控制论]