An inverse-free dynamical system for solving the absolute value equations

被引：41
作者：
Chen, Cairong [1 ,2 ]
Yang, Yinong [3 ]
Yu, Dongmei [4 ,5 ]
Han, Deren [5 ]
机构：
[1] Fujian Normal Univ, Coll Math & Informat, FJKLMAA, Fuzhou 350007, Peoples R China
[2] Fujian Normal Univ, Ctr Appl Math Fujian Prov, Fuzhou 350007, Peoples R China
[3] Liaoning Univ, Sch Math, Shenyang 110036, Peoples R China
[4] Liaoning Tech Univ, Inst Optimizat & Decis Analyt, Fuxin 123000, Peoples R China
[5] Beihang Univ, Sch Math Sci, LMIB, Beijing 100191, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2021年 / 168卷
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Absolute value equation; Dynamical system; Globally asymptotically stable; Equilibrium point; Inverse-free; Numerical simulation; NEURAL-NETWORK; ITERATION METHOD; NEWTON METHOD; MODEL; COMPLEMENTARITY; BOUNDS;
D O I：
10.1016/j.apnum.2021.06.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an inverse-free dynamical system is built to solve the absolute value equations (AVEs), whose equilibrium points coincide with the solutions of the AVEs. Under proper assumptions, the equilibrium points of the dynamical system exist and could be (globally) asymptotically stable. In addition, with strongly monotone property, a global projection-type error bound is provided to estimate the distance between any trajectories and the unique equilibrium point. Compared with four existing dynamical systems for solving the AVEs, our method is inverse-free and is still valid even if 1 is an eigenvalue of the coefficient matrix. Some numerical simulations are given to show the effectiveness of the proposed method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：170 / 181
页数：12
相关论文
共 50 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]   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]   The forward-backward-forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces [J].
Bot, R., I ;
Csetnek, E. R. ;
Vuong, P. T. .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2020, 287 (01) :49-60
[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]   Nash equilibria, variational inequalities, and dynamical systems [J].
Cavazzuti, E ;
Pappalardo, M ;
Passacantando, M .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 114 (03) :491-506
[7]  
Chen C.-L., 2020, ARXIV PREPRINT ARXIV
[8]  
Chen C.-R., ARXIV PREPRINT ARXIV, P2021
[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]   An efficient projection neural network for solving bilinear programming problems [J].
Effati, Sohrab ;
Mansoori, Amin ;
Eshaghnezhad, Mohammad .
NEUROCOMPUTING, 2015, 168 :1188-1197
12345