A class of matrix splitting-based fixed-point iteration method for the vertical nonlinear complementarity problem

被引：0
作者：
Yapeng Wang [1 ]
Xuewen Mu [1 ]
机构：
[1] School of Mathematics and Statistics, Xidian University, Shanxi, Xian
来源：
Computational and Applied Mathematics | 2025年 / 44卷 / 5期
关键词：
Convergence; Fixed point iteration; Vertical nonlinear complementarity problem;
D O I：
10.1007/s40314-025-03212-z
中图分类号：
学科分类号：
摘要：
In this paper, we propose a class of matrix splitting-based fixed-point iteration (FPI) methods for solving the vertical nonlinear complementarity problem (VNCP). Under appropriate conditions, we present two convergence results obtained using different techniques and estimate the number of iterations required for the FPI method. Additionally, through numerical experiments, we demonstrated that the FPI method surpasses other methods in computational efficiency. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2025.
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  • [1] Ali R., Pan K., Two new fixed point iterative schemes for absolute value equations, Jpn J Ind Appl Math, 40, 1, pp. 303-314, (2023)
  • [2] Ali R., Ali A., Alam M.M., Et al., (2022) Numerical solution of the absolute value equations using two matrix splitting fixed point iteration methods, J Funct Spaces, 1, (2022)
  • [3] Bai Z.Z., Pan JY, (2021)
  • [4] Bai Z.Z., Modulus-based matrix splitting iteration methods for linear complementarity problems, Numerical Linear Algebra with Applications, 17, 6, pp. 917-933, (2010)
  • [5] Brogliato B., Some perspectives on the analysis and control of complementarity systems, IEEE Trans Autom Control, 48, 6, pp. 918-935, (2003)
  • [6] Dai P.F., A fixed point iterative method for tensor complementarity problems, J Sci Comput, 84, 3, (2020)
  • [7] Do Y., Kim S.D., Kim P.S., Stability of fixed points placed on the border in the piecewise linear systems, Chaos, Solitons & Fractals, 38, 2, pp. 391-399, (2008)
  • [8] Facchinei F., Finite-dimensional variational inequalities and complementarity problems, (2003)
  • [9] Fang X.M., General fixed point method for solving the linear complementarity problem, AIMS Math, 6, 11, pp. 11904-11920, (2021)
  • [10] Fu Z.F., Wu S.L., Li L., New modulus-based matrix splitting method for the vertical nonlinear complementarity problem, J Comput Appl Math, 457, (2025)
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