一种求解非线性方程组的改进Shamanskii-like Levenberg-Marquardt算法  

A new modified efficient Shamanskii-like Levenberg-Marquardt method for solving systems of nonlinear equations

作　　者：房明磊 丁德凤 王敏 盛雨婷 FANG Minglei;DING Defeng;WANG Ming;SHENG Yuting(School of Mathmatics and Big Data,Anhui University of Science and Technology,Huainan 232001,Anhui,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《山东大学学报（理学版）》2023年第8期118-126,共9页Journal of Shandong University(Natural Science)

基　　金：安徽省高校自然科学基金资助项目(KJ2021A0451);安徽省自然科学基金资助项目(2008085MA01)。

摘　　要：在Shamanskii-like Levenberg-Marquardt(SLM)算法中引入参数,得到一种改进的SLM算法,在m阶非单调Armijo线搜索下证明所提出的算法具有全局收敛性,并且有m+1阶收敛率。数值实验表明,算法对于求解非线性方程组大规模问题有效。A new Shamanskii-like Levenberg-Marquardt method(SLM)to solve systems of nonlinear equations is presented by introducing parameters in this paper.With m order nonmonotone Armijo line search,the global convergence of the new algorithm is proved and the convergence rate of whom is shown to be m+1.Numerical experiments demonstrate that the new algorithm can solve large scale problems effectively.

关 键 词：无约束优化 ARMIJO线搜索 Shamanskii-like LEVENBERG-MARQUARDT算法 非线性方程组 

分 类 号：O221.2[理学—运筹学与控制论]