Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

doi:10.1007/s42967-023-00311-8

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (4): 1308-1332.doi: 10.1007/s42967-023-00311-8

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Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

Lu-Xin Wang^1,2, Qin-Qin Shen³, Yang Cao^1,3

1. School of Information Science and Technology, Nantong University, Nantong, 226019, Jiangsu, China;
2. Department of Basic Teaching, Jiangsu Shipping College, Nantong, 226010, Jiangsu, China;
3. School of Transportation and Civil Engineering, Nantong University, Nantong, 226019, Jiangsu, China

收稿日期:2023-06-07 修回日期:2023-08-18 接受日期:2023-08-20 出版日期:2023-11-23 发布日期:2023-11-23
通讯作者: Qin-Qin Shen,E-mail:shenqq@ntu.edu.cn E-mail:shenqq@ntu.edu.cn
作者简介:Lu-Xin Wang, E-mail:wangluxin@jssc.edu.cn;Yang Cao, E-mail:caoyangnt@ntu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (No. 11771225), the Qinglan Project of Jiangsu Province of China and the Science and Technology Project of Nantong City of China (No. JC2021198).

Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

Lu-Xin Wang^1,2, Qin-Qin Shen³, Yang Cao^1,3

1. School of Information Science and Technology, Nantong University, Nantong, 226019, Jiangsu, China;
2. Department of Basic Teaching, Jiangsu Shipping College, Nantong, 226010, Jiangsu, China;
3. School of Transportation and Civil Engineering, Nantong University, Nantong, 226019, Jiangsu, China

Received:2023-06-07 Revised:2023-08-18 Accepted:2023-08-20 Online:2023-11-23 Published:2023-11-23
Supported by:
This work was supported by the National Natural Science Foundation of China (No. 11771225), the Qinglan Project of Jiangsu Province of China and the Science and Technology Project of Nantong City of China (No. JC2021198).

摘要/Abstract

摘要： In this paper, the modulus-based matrix splitting (MMS) iteration method is extended to solve the horizontal quasi-complementarity problem (HQCP), which is characterized by the presence of two system matrices and two nonlinear functions. Based on the specific matrix splitting of the system matrices, a series of MMS relaxation iteration methods are presented. Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H₊-matrices, respectively. Finally, two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.

关键词: Horizontal quasi-complementarity problem (HQCP), Modulus-based method, Matrix splitting, Convergence

Abstract: In this paper, the modulus-based matrix splitting (MMS) iteration method is extended to solve the horizontal quasi-complementarity problem (HQCP), which is characterized by the presence of two system matrices and two nonlinear functions. Based on the specific matrix splitting of the system matrices, a series of MMS relaxation iteration methods are presented. Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H₊-matrices, respectively. Finally, two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.

Key words: Horizontal quasi-complementarity problem (HQCP), Modulus-based method, Matrix splitting, Convergence

中图分类号:

65F10
65F50

Lu-Xin Wang, Qin-Qin Shen, Yang Cao. Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1308-1332.

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Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

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