AN INEXACT RELAXED GENERALIZED NEWTON ITERATIVE METHOD FOR SOLVING GENERALIZED ABSOLUTE VALUE EQUATIONS

被引：0

作者：

Yu, Dongmei ^{[1
]}

Zhang, Yiming ^{[2
,3
]}

Yuan, Yifei ^{[4
]}

机构：

[1] Liaoning Tech Univ, Coll Sci Inst Optimizat & Decis Analyt, Sch Business Adm, Fuxin 123000, Peoples R China

[2] Liaoning Tech Univ, Sch Business Adm, Huludao 125105, Peoples R China

[3] Liaoning Tech Univ, Inst Optimizat & Decis Analyt, Fuxin 123000, Peoples R China

[4] Liaoning Tech Univ, Inst Optimizat & Decis Anal, Coll Sci, Fuxin 123000, Peoples R China

来源：

PACIFIC JOURNAL OF OPTIMIZATION | 2024年 / 20卷 / 01期

基金：

中国国家自然科学基金;

关键词：

generalized absolute value equations; generalized Newton method; relaxed; inexact; convergence; LINEAR COMPLEMENTARITY; VERTICAL-BAR; ALGORITHM; MODEL;

D O I：

暂无

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, for solving the generalized absolute value equations (GAVE), an inexact relaxed generalized Newton (IRGN) iterative method is developed, which can adopt a relative error tolerance. Linear convergence of the IRGN iterative method is established under suitable conditions, and theoretical analysis of the inexact schemes support the efficient computational implementations of the exact schemes. It has been found that the IRGN iterative method involves the classical generalized Newton (GN) iterative method as a special case. Some numerical results are given to demonstrate the viability and robustness of the proposed methods.

引用

页码：23 / 44

页数：22

共 45 条

[1] Solving absolute value equation using complementarity and smoothing functions [J].

Abdallah, L. ;

Haddou, M. ;

Migot, T. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 327 :196-207

[2] A novel generalization of the natural residual function and a neural network approach for the NCP [J].

Alcantara, Jan Harold ;

Chen, Jein-Shan .

NEUROCOMPUTING, 2020, 413 :368-382

[3] Modulus-based matrix splitting iteration methods for linear complementarity problems [J].

Bai, Zhong-Zhi .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2010, 17 (06) :917-933

[4] On the global convergence of the inexact semi-smooth Newton method for absolute value equation [J].

Bello Cruz, J. Y. ;

Ferreira, O. P. ;

Prudente, L. F. .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2016, 65 (01) :93-108

[5] A globally and quadratically convergent method for absolute value equations [J].

Caccetta, Louis ;

Qu, Biao ;

Zhou, Guanglu .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2011, 48 (01) :45-58

[6] An inverse-free dynamical system for solving the absolute value equations [J].

Chen, Cairong ;

Yang, Yinong ;

Yu, Dongmei ;

Han, Deren .

APPLIED NUMERICAL MATHEMATICS, 2021, 168 :170-181

[7] Benchmarking optimization software with performance profiles [J].

Dolan, ED ;

Moré, JJ .

MATHEMATICAL PROGRAMMING, 2002, 91 (02) :201-213

[8] A new SOR-like method for solving absolute value equations [J].

Dong, Xu ;

Shao, Xin-Hui ;

Shen, Hai-Long .

APPLIED NUMERICAL MATHEMATICS, 2020, 156 :410-421

[9] A generalization of the Gauss-Seidel iteration method for solving absolute value equations [J].

Edalatpour, Vahid ;

Hezari, Davod ;

Salkuyeh, Davod Khojasteh .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 :156-167

[10] METHODS OF CONJUGATE GRADIENTS FOR SOLVING LINEAR SYSTEMS [J].

HESTENES, MR ;

STIEFEL, E .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS, 1952, 49 (06) :409-436

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