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

作　　者：CHEN Liang MA Yanfang 

机构地区：[1]School of Mathematical Sciences,Huaibei Normal University,Huaibei 235000,China [2]School of Compuler Science and Technology,Huaibei Normal University,Huaibei 235000,China

出　　处：《Journal of Systems Science & Complexity》2020年第5期1694-1707,共14页系统科学与复杂性学报（英文版）

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。

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.

关 键 词：Armijo line search Levenberg-Marquardt method local error bound condition systems of nonlinear equations unconstrained optimization 

分 类 号：O241.7[理学—计算数学]