An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems

被引：0

作者：

Li, Xuehua ^{[1
]}

Chen, Cairong ^{[1
]}

机构：

[1] Fujian Normal Univ, Sch Math & Stat, FJKLMAA, Fuzhou 350117, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 457卷

关键词：

Generalized absolute value equations; Matrix splitting; Generalized Newton-based method; Convergence; VERTICAL-BAR; ITERATION METHOD; AX;

D O I：

10.1016/j.cam.2024.116329

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

引用

页数：15

共 49 条

[1] SOLVING ABSOLUTE VALUE EQUATIONS VIA COMPLEMENTARITY AND INTERIOR-POINT METHODS [J].

Achache, Mohamed ;

Hazzam, Nadia .

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018, 2018

[2] Method of alternating projections for the general absolute value equation [J].

Alcantara, Jan Harold ;

Chen, Jein-Shan ;

Tam, Matthew K. .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2023, 25 (01)

[3] 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

[4] 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

[5] A NON-MONOTONE SMOOTHING NEWTON ALGORITHM FOR SOLVING THE SYSTEM OF GENERALIZED ABSOLUTE VALUE EQUATIONS [J].

Chen, Cairong ;

Yu, Dongmei ;

Han, Deren ;

Ma, Changfeng .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2025, 43 (02) :438-460

[6] Exact and inexact Douglas-Rachford splitting methods for solving large-scale sparse absolute value equations [J].

Chen, Cairong ;

Yu, Dongmei ;

Han, Deren .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2023, 43 (02) :1036-1060

[7]

Cottle RW, 2009, CLASS APPL MATH, V60, P1, DOI 10.1137/1.9780898719000

[8]

Golub GeneH., 1996, MATRIX COMPUTATIONS

[9] Comments on finite termination of the generalized Newton method for absolute value equations [J].

Guo, Chun-Hua .

OPTIMIZATION LETTERS, 2025, 19 (05) :1017-1026

[10]

Hladik M, 2024, Arxiv, DOI arXiv:2404.06319

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