A PARAMETER-SELF-ADJUSTING LEVENBERG-MARQUARDT METHOD FOR SOLVING NONSMOOTH EQUATIONS  

作　　者：Liyan Qi XiantaoXiao Liwei Zhang 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology and School of Sciences, Dalian Ocean University, Dalian 116025, China [2]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

出　　处：《Journal of Computational Mathematics》2016年第3期317-338,共22页计算数学（英文）

基　　金：Acknowledgments. This work is supported by the National Natural Science Foundation of China under projects Nos. 11071029, 11101064 and 91130007 and speciMized Research Fund for the Doctoral Program of Higher Education （20110041120039）. We are grateful to the associate editor and anonymous referee＇s comments to improve the quality of the manuscript. The second author also appreciate the discussion with his student Miao Xiaonan.

摘　　要：A parameter-self-adjusting Levenberg-Marquardt method （PSA-LMM） is proposed for solving a nonlinear system of equations F（x） = 0, where F ：R^n→R^n is a semismooth mapping. At each iteration, the LM parameter μk is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA- LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.A parameter-self-adjusting Levenberg-Marquardt method （PSA-LMM） is proposed for solving a nonlinear system of equations F（x） = 0, where F ：R^n→R^n is a semismooth mapping. At each iteration, the LM parameter μk is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA- LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.

关 键 词：Levenberg-Marquardt method Nonsmooth equations Nonlinear complemen-tarity problems. 

分 类 号：O343.3[理学—固体力学] TB566[理学—力学]