一种新的非单调修正Levenberg-Marquardt算法  

A New Nonmonotone Modified Levenberg-marquardt Algorithm

作　　者：晋慧慧 袁柳洋[1,2] 万仲平 JIN HUIHUI;YUAN LIUYANG;WAN ZHONGPING(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process,Wuhan University of Science and Technology,Wuhan 430065,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,武汉430065 [2]冶金工业过程系统科学湖北省重点实验室(武汉科技大学),武汉430065 [3]武汉大学数学与统计学院,武汉430072

出　　处：《应用数学学报》2024年第5期799-810,共12页Acta Mathematicae Applicatae Sinica

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。

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.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 modifed 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 

分 类 号：O221[理学—运筹学与控制论]