Shamanskii-Like Levenberg-Marquardt Method with a New Line Search for Systems of Nonlinear Equations

作     者：CHEN Liang MA Yanfang CHEN Liang;MA Yanfang

作者机构：School of Mathematical SciencesHuaibei Normal UniversityHuaibei 235000China School of Compuler Science and TechnologyHuaibei Normal UniversityHuaibei 235000China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2020年第33卷第5期

页      面：1694-1707页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 070102[理学-计算数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the Natural Science Foundation of Anhui Province under Grant No.1708085MF159 the Natural Science Foundation of the Anhui Higher Education Institutions under Grant Nos.KJ2017A375 KJ2019A0604 the abroad visiting of excellent young talents in universities of Anhui province under Grant No.GXGWFX2019022。 

主　　题：Armijo line search Levenberg-Marquardt method local error bound condition systems of nonlinear equations unconstrained optimization 

摘      要：To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.