A TWO-STEP MODULUS-BASED MULTISPLITTING ITERATION METHOD FOR THE NONLINEAR COMPLEMENTARITY PROBLEM

Guangbin Wang; Fuping Tan

doi:10.11948/20190290

2020 Volume 10 Issue 5

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Guangbin Wang, Fuping Tan. A TWO-STEP MODULUS-BASED MULTISPLITTING ITERATION METHOD FOR THE NONLINEAR COMPLEMENTARITY PROBLEM[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1954-1961. doi: 10.11948/20190290

Citation:

Guangbin Wang, Fuping Tan. A TWO-STEP MODULUS-BASED MULTISPLITTING ITERATION METHOD FOR THE NONLINEAR COMPLEMENTARITY PROBLEM[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1954-1961. doi: 10.11948/20190290

A TWO-STEP MODULUS-BASED MULTISPLITTING ITERATION METHOD FOR THE NONLINEAR COMPLEMENTARITY PROBLEM

Guangbin Wang^1, ,,
Fuping Tan²

1.
Department of Mathematics, Qingdao Agricultural University, No.700 Changcheng Road, 266109 Qingdao, China
2.
Department of Mathematics, Shanghai University, No.99 Shangda Road, 200444 Shanghai, China

Corresponding author: Email: wguangbin750828@sina.com (G. Wang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 11771275) and the Science and Technology Program of Shandong Universities (No. J16LI04) and the Advanced Talents Foundation of QAU (No. 6631115047)

Abstract

Abstract

In this paper, we construct a two-step modulus-based multisplitting iteration method based on multiple splittings of the system matrix for the nonlinear complementarity problem. And we prove its convergence when the system matrix is an $ H $-matrix with positive diagonal elements. Numerical experiments show that the proposed method is efficient.
- Two-step /
- modulus-based multisplitting method /
- nonlinear complementarity problem /
- H-matrix
MSC: 65F10, 15B99

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References

[1]	Z. Bai, Modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl., 2010, 17(6), 917-933. doi: 10.1002/nla.680 CrossRef Google Scholar
[2]	Z. Bai and L. Zhang, Modulus-based synchronous multisplitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl., 2013, 20(3), 425-439. doi: 10.1002/nla.1835 CrossRef Google Scholar
[3]	A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences, SIAM, Philadelphia, 1994. Google Scholar
[4]	A. Hadjidimos and L. Zhang, Comparison of three classes of algorithms for the solution of the linear complementarity problem with an ${H}_+$-matrix, J. Comput. Appl. Math., 2018, 336(1), 175-191. Google Scholar
[5]	B. Huang and C. Ma, Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems, Comp. Appl. Math., 2018, 37(3), 3053-3076. doi: 10.1007/s40314-017-0496-z CrossRef Google Scholar
[6]	Y. Ke and C. Ma, On the convergence analysis of two-step modulus-based matrix splitting iteration method for linear complementarity problems, Appl. Math. Comput., 2014, 243(1), 413-418. Google Scholar
[7]	Y. Ke, C. Ma and H. Zhang, The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems, Numer. Algor., 2018, 79(4), 1283-1303. doi: 10.1007/s11075-018-0484-4 CrossRef Google Scholar
[8]	Y. Ke, C. Ma and H. Zhang, The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems, Comp. Appl. Math., 2018, 37(5), 6795-6820. doi: 10.1007/s40314-018-0687-2 CrossRef Google Scholar
[9]	R. Li, Y. Wang and J. Yin, On the convergence of two-step modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems with ${H}_+$-matrices, Numer. Math. Theor. Meth. Appl., 2018, 11(1), 128-139. Google Scholar
[10]	R. Li and J. Yin, Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems, Numer. Algor., 2017, 75(2), 339-358. doi: 10.1007/s11075-016-0243-3 CrossRef Google Scholar
[11]	W. Li, A general modulus-based matrix splitting method for linear complementarity problems of ${H}$-matrices, Appl. Math. Lett., 2013, 26(12), 1159-1164. doi: 10.1016/j.aml.2013.06.015 CrossRef Google Scholar
[12]	W. Li and H. Zheng, A preconditioned modulus-based iteration method for solving linear complementarity problems of ${H}$-matrices, Linear and Multilinear Algebra, 2016, 64(7), 1-14. Google Scholar
[13]	Z. Xia and C. Li, Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem, Appl. Math. Comput., 2015, 271(1), 34-42. Google Scholar
[14]	W. Xu and H. Liu, A modified general modulus-based matrix splitting method for linear complementarity problems of ${H}$-matrices, Linear Algebra Appl., 2014, 458(10), 626-637. Google Scholar
[15]	N. Zheng and J. Yin, Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an ${H}_+$-matrix, J. Comput. Appl. Math., 2014, 260(2), 281-293. Google Scholar