Improved convergence results for a modified Levenberg-Marquardt method for nonlinear equations and applications in MPCC

被引：18

作者：

Zhu, Xide ^{[1
]}

Lin, Gui-Hua ^{[2
]}

机构：

[1] Yokohama Natl Univ, Fac Business Adm, Hodogaya Ku, 79-4 Tokiwadai, Yokohama, Kanagawa 2408501, Japan

[2] Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China

来源：

OPTIMIZATION METHODS & SOFTWARE | 2016年 / 31卷 / 04期

基金：

国家教育部科学基金资助;

关键词：

nonlinear equations; Levenberg-Marquardt method; MPCC; C-; M-; S-stationarity; superlinear convergence; MATHEMATICAL PROGRAMS; EQUILIBRIUM CONSTRAINTS; LOCAL CONVERGENCE; OPTIMALITY;

D O I：

10.1080/10556788.2016.1171863

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we first consider a modified Levenberg-Marquardt method for solving nonlinear equations and show that the method converges superlinearly to a solution of the nonlinear equations under suitable conditions. Then, we reformulate the C-/M-/S-stationarity conditions of mathematical program with complementarity constraints as nonlinear equations so that we may employ the modified Levenberg-Marquardt method to solve these stationarity systems. Preliminary numerical experiments show that the new approach is promising.

引用

页码：791 / 804

页数：14

共 50 条

[1] Improved convergence results of an efficient Levenberg-Marquardt method for nonlinear equations
Zeng, Meilan
Zhou, Guanghui
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (06) : 3655 - 3671
[2] THE MODIFIED LEVENBERG-MARQUARDT METHOD FOR NONLINEAR EQUATIONS WITH CUBIC CONVERGENCE
Fan, Jinyan
[J]. MATHEMATICS OF COMPUTATION, 2012, 81 (277) : 447 - 466
[3] ACCELERATING THE MODIFIED LEVENBERG-MARQUARDT METHOD FOR NONLINEAR EQUATIONS
Fan, Jinyan
[J]. MATHEMATICS OF COMPUTATION, 2014, 83 (287) : 1173 - 1187
[4] On the global convergence of a Levenberg-Marquardt method for constrained nonlinear equations
Yu Z.
[J]. Journal of Applied Mathematics and Computing, 2004, 16 (1-2) : 183 - 194
[5] Improved convergence results of an efficient Levenberg–Marquardt method for nonlinear equations
Meilan Zeng
Guanghui Zhou
[J]. Journal of Applied Mathematics and Computing, 2022, 68 : 3655 - 3671
[6] ???????A New Modified Levenberg-Marquardt Method for Systems of Nonlinear Equations
Chen, Liang
Ma, Yanfang
[J]. JOURNAL OF MATHEMATICS, 2023, 2023
[7] A modified Levenberg-Marquardt method for solving system of nonlinear equations
Chen, Liang
Ma, Yanfang
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (02) : 2019 - 2040
[8] A modified Levenberg-Marquardt method with line search for nonlinear equations
Chen, Liang
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2016, 65 (03) : 753 - 779
[9] A modified two steps Levenberg-Marquardt method for nonlinear equations
Amini, Keyvan
Rostami, Faramarz
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 288 : 341 - 350
[10] The convergence of a Levenberg-Marquardt method for nonlinear inequalities
Yin, Hongxia
Huang, Zheng-Hai
Qi, Liqun
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (5-6) : 687 - 716

← 1 2 3 4 5 →