求解一类新的广义绝对值方程组的动力学模型

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 818-825.

求解一类新的广义绝对值方程组的动力学模型

郑雯丽,唐嘉*(),陈彩荣

^{福建师范大学数学与统计学院福州 350007}

收稿日期:2021-08-23 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 唐嘉 E-mail:tang_jia@126.com
基金资助:
福建省自然科学基金面上资助项目(2020J01166);福建省自然科学基金面上资助项目(2021J01661);国家自然科学基金青年基金(11901024)

A Dynamic Model for a Class of New Generalized Absolute Value Equations

Wenli Zheng,Jia Tang*(),Cairong Chen

^{School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007}

Received:2021-08-23 Online:2022-06-26 Published:2022-05-09
Contact: Jia Tang E-mail:tang_jia@126.com
Supported by:
the NSF of Fujian Province(2020J01166);the NSF of Fujian Province(2021J01661);the NSFC(11901024)

摘要/Abstract

摘要：

该文提出了求解一类新的广义绝对值方程组（GAVE）的动力学模型.在适当的条件下，证明了GAVE的解等价于动力学模型的平衡点，并证明了平衡点的渐近稳定性.数值实验验证了所提出的模型是可行且有效的.

关键词: 广义绝对值方程组, 线性互补问题, 动力学模型, 平衡点, 稳定性

Abstract:

In this paper, a dynamic model for solving a class of new generalized absolute value equations (GAVE) is proposed. Under suitable conditions, it can be proved that the solution of the GAVE is equivalent to the equilibrium point of the dynamic model and that the equilibrium point of the dynamic model is asymptotically stable. Numerical experiments show that the proposed dynamic model is feasible and effective.

Key words: Generalized absolute value equation, Linear complementarity problem, Dynamic model, Equilibrium point, stability

中图分类号:

O241.6

郑雯丽,唐嘉,陈彩荣. 求解一类新的广义绝对值方程组的动力学模型[J]. 数学物理学报, 2022, 42(3): 818-825.

Wenli Zheng,Jia Tang,Cairong Chen. A Dynamic Model for a Class of New Generalized Absolute Value Equations[J]. Acta mathematica scientia,Series A, 2022, 42(3): 818-825.

参考文献

1	Bai Z Z . Modulus-based matrix splitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications, 2010, 17, 917- 933
2	Cottle R W , Pang J S , Stone R E . The Linear Complementarity Problem. Boston: Academic Press, 1992
3	Chen C R , Yang Y N , Yu D M , et al. An inverse-free dynamical system for solving the absolute value equations. Applied Numerical Mathematics, 2021, 168, 170- 181
4	Gao X B , Wang J . Analysis and application of a one-layer neural network for solving horizontal linear complementarity problems. International Journal of Computational Intelligence Systems, 2014, 7 (4): 724- 732
5	He B S . Inexact implicit methods for monotone general variational inequalities. Mathematical Programming, 1999, 86 (1): 199- 217
6	Khalil H K . Nonlinear Systems. Michigan: Prentice-Hall, 1996
7	Kinderlehrer D , Stampcchia G . An Introduction to Variational Inequalities and Their Applications. New York: Academic Press, 1980
8	Mangasarian O L . Absolute value programming. Computational Optimization and Applications, 2007, 36 (1): 43- 53
9	Mansoori A , Erfanian M . A dynamic model to solve the absolute value equation. Journal Computational and Applied Mathematics, 2018, 333, 28- 35
10	Mangasarian O L , Meyer R R . Absolute value equations. Linear Algebra and Applications, 2006, 419 (2/3): 359- 367
11	Prokopyev O . On equivalent reformulations for absolute value equations. Computational Optimization and Applications, 2009, 44 (3): 363- 372
12	Rohn J . A theorem of the alternatives for the equation $Ax+B\|x\|=b$. Linear Multilinear Algebra, 2004, 52 (6): 421- 426
13	Rohn J . Systems of linear interval equations. Linear Algebra and Applications, 1989, 126, 39- 78
14	Wu S L . The unique solution of a class of the new generalized absolute value equation. Applied Mathematics Letters, 2021, 116 (1): 107029
15	Wu S L , Li C X . A class of new modulus-based matrix splitting methods for linear complementarity problem. Optimization Letters, 2021,

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