Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (3): 1246-1254.
Previous Articles Next Articles
Shuhong Wen1(
), Yifen Ke2,*(
), Lifen Xiao2(
), Xiwen Chen2(
)
Received:2025-01-04
Revised:2025-10-21
Online:2026-06-26
Published:2026-06-16
Contact:
Yifen Ke
E-mail:32642217@qq.com;keyifen@fjnu.edu.cn;1943488318@qq.com;2513758118@qq.com
Supported by:CLC Number:
Shuhong Wen, Yifen Ke, Lifen Xiao, Xiwen Chen. A Modulus-Based Matrix Splitting Iterative Method for a Class of Vertical Linear Complementarity Problems[J].Acta mathematica scientia,Series A, 2026, 46(3): 1246-1254.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| [1] | Cottle R W, Pang J S., Stone R E. The Linear Complementarity Problem. San Diego: Academic, 1992 |
| [2] |
Sznajder R, Gowda M S. Generalizations of $P_0$-and $P$-properties; extended vertical and horizontal linear complementarity problems. Linear Algebra and its Applications, 1995, 223/224: 695-715
doi: 10.1016/0024-3795(93)00184-2 |
| [3] |
Gowda M S, Sznajder R. A generalization of the Nash equilibrium theorem on bimatrix games. International Journal of Game Theory, 1996, 25: 1-12
doi: 10.1007/BF01254380 |
| [4] |
Zhang L P, Gao Z Y. Global linear and quadratic one-step smoothing Newton method for vertical linear complementarity problems. Applied Mathematics and Mechanics, 2003, 24: 738-746
doi: 10.1007/BF02437876 |
| [5] |
Nagae T, Akamatsu T. A generalized complementarity approach to solving real option problems. Journal of Economic Dynamics and Control, 2008, 32(6): 1754-1779
doi: 10.1016/j.jedc.2007.04.010 |
| [6] |
Sun M. Monotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems. Journal of Mathematical Analysis and Applications, 1989, 144(2): 474-485
doi: 10.1016/0022-247X(89)90347-8 |
| [7] |
Qi H D, Liao L Z. A smoothing Newton method for extended vertical linear complementarity problems. SIAM Journal on Matrix Analysis and Applications, 1999, 21(1): 45-66
doi: 10.1137/S0895479897329837 |
| [8] |
Peng J M, Lin Z. A non-interior continuation method for generalized linear complementarity problems. Mathematical Programming, 1999, 86(3): 533-563
doi: 10.1007/s101070050104 |
| [9] | Mohan S R, Neogy S K, Sridhar R. The generalized linear complementarity problem revisited. Mathematica Program, 1996, 74(2): 197-218 |
| [10] | Van Bokhoven W M G. Piecewise-Linear Modelling and Analysis.Eindhoven: Proefschrift, 1981 |
| [11] |
Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications, 2010, 17(6): 917-933
doi: 10.1002/nla.v17.6 |
| [12] |
Bai Z Z, Zhang L L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications, 2013, 20(3): 425-439
doi: 10.1002/nla.v20.3 |
| [13] | Bai Z Z, Zhang L L. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numerical Algorithms, 2013, 62(1): 59-77 |
| [14] | Wu S L, Li C X. Two-sweep modulus-based matrix splitting iteration methods for linear complementarity problems. Journal of Computational Mathematics, 2016, 302: 327-339 |
| [15] |
Ma C F, Huang N. Modifed modulus-based matrix splitting algorithms for a class of weakly nondiferentiable nonlinear complementarity problems. Applied Numerical Mathematics, 2016, 108: 116-124
doi: 10.1016/j.apnum.2016.05.004 |
| [16] |
Huang N, Ma C F. The modulus-based matrix splitting algorithms for a class of weakly nondifferentiable nonlinear complementarity problems. Numerical Linear Algebra with Applications, 2016, 23(3): 558-569
doi: 10.1002/nla.v23.3 |
| [17] |
Wu S L, Li L. New modulus-based matrix splitting methods for implicit complementarity problem. Numerical Algorithms, 2022, 90(4): 1735-1754
doi: 10.1007/s11075-021-01249-9 |
| [18] | 黎科良, 柯艺芬, 马昌凤. 求解一类隐式互补问题的加速模系矩阵分裂迭代方法. 应用数学, 2023, 36(4): 1025-1033 |
| Li K L, Ke Y F, Ma C F. Accelerated modulus-based matrix splitting iteration method for solving a class of implicit complementarity problems. Mathematica Applicata, 2023, 36(4): 1025-1033 | |
| [19] |
Wu S L, Guo P. Modulus-based matrix splitting algorithms for the quasi-complementarity problems. Applied Numerical Mathematics, 2018, 132: 127-137
doi: 10.1016/j.apnum.2018.05.017 |
| [20] |
Mezzadri F, Galligani E. Modulus-based matrix splitting methods for horizontal linear complementarity problems. Numerical Algorithms, 2020, 83: 201-219
doi: 10.1007/s11075-019-00677-y |
| [21] |
Ke Y F, Ma C F, Zhang H. The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems. Numerical Algorithms, 2018, 79(4): 1283-1303
doi: 10.1007/s11075-018-0484-4 |
| [22] |
李枝枝, 柯艺芬, 储日升, 等. 二阶锥线性互补问题的广义模系矩阵分裂迭代算法. 计算数学, 2019, 41(4): 395-405
doi: 10.12286/jssx.2019.4.395 |
|
Li Z Z, Ke Y F, Chu R S, et al. Generalized modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems. Mathematica Numerica Sinica, 2019, 41(4): 395-405
doi: 10.12286/jssx.2019.4.395 |
|
| [23] |
Ke Y F, Ma C F, Zhang H. The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems. Computational and Applied Mathematics, 2018, 37(5): 6795-6820
doi: 10.1007/s40314-018-0687-2 |
| [24] |
Mezzadri F. A modulus-based formulation for the vertical linear complementarity problem. Numerical Algorithms, 2022, 90(4): 1547-1568
doi: 10.1007/s11075-021-01240-4 |
| [25] | Guo W X, Zheng H, Peng X F. New convergence results of the modulus-based methods for vertical linear complementarity problems. Applied Mathematics Letters, 2023, 135: Art 108444 |
| [26] | Wang D, Li J C. Relaxation modulus-based matrix splitting iteration method for vertical linear complementarity problem. Journal of Computational and Applied Mathematics, 2024, 437: Art 115430 |
| [27] |
Li C X, Wu S L. A class of new modulus-based matrix splitting methods for linear complementarity problem. Optimization Letters, 2022, 5: 1-17
doi: 10.1007/s11590-010-0228-4 |
|
||