Search Advanced

Electronic Research Archive

2022, Volume 30, Issue 3: 1062-1074. doi: 10.3934/era.2022056
Previous Article Next Article
Research article Special Issues

A generalization of the AOR iteration method for solving absolute value equations

  • School of Mathematics, Yunnan Normal University, Kunming 650500, China
  • Received: 07 December 2021 Revised: 25 February 2022 Accepted: 07 March 2022 Published: 09 March 2022

  • In this paper, based on the accelerated over relaxation (AOR) iteration method, a generalization of the AOR iteration method is presented to solve the absolute value equations (AVE), which is called the GAOR method. The convergence conditions of the GAOR method are obtained. Numerical experiments are presented in order to verify the feasibility of the GAOR method.

    Citation: Cui-Xia Li. A generalization of the AOR iteration method for solving absolute value equations[J]. Electronic Research Archive, 2022, 30(3): 1062-1074. doi: 10.3934/era.2022056

    Related Papers:

  • In this paper, based on the accelerated over relaxation (AOR) iteration method, a generalization of the AOR iteration method is presented to solve the absolute value equations (AVE), which is called the GAOR method. The convergence conditions of the GAOR method are obtained. Numerical experiments are presented in order to verify the feasibility of the GAOR method.


    加载中


    [1] J. Rohn, A theorem of the alternatives for the equation $Ax+B|x| = b$, Linear Multilinear A., 52 (2004), 421–426. https://doi.org/10.1080/0308108042000220686 doi: 10.1080/0308108042000220686
    [2] O. L. Mangasarian, Absolute value programming, Comput. Optim. Appl., 36 (2007), 43–53. https://doi.org/10.1007/s10589-006-0395-5 doi: 10.1007/s10589-006-0395-5
    [3] O. L. Mangasarian, Absolute value equations via concave minimization, Optim. Lett., 1 (2007), 1–8. https://doi.org/10.1007/s11590-006-0005-6 doi: 10.1007/s11590-006-0005-6
    [4] R. W. Cottle, G. B. Dantzig, Complementary pivot theory of mathematical programming, Linear Algebra Appl., 1 (1968), 103–125. https://doi.org/10.1016/0024-3795(68)90052-9 doi: 10.1016/0024-3795(68)90052-9
    [5] R. W. Cottle, J. S. Pang, R. E. Stone, The Linear Complementarity Problem, Academic, San Diego, 1992. https://doi.org/10.1007/978-94-015-8330-5_3
    [6] O. L. Mangasarian, A generalized Newton method for absolute value equations, Optim. Lett., 3 (2009), 101–108. https://doi.org/10.1007/s11590-008-0094-5 doi: 10.1007/s11590-008-0094-5
    [7] L. Caccetta, B. Qu, G. L. Zhou, A globally and quadratically convergent method for absolute value equations, Comput. Optim. Appl., 48 (2011), 45–58. https://doi.org/10.1007/s10589-009-9242-9 doi: 10.1007/s10589-009-9242-9
    [8] S. L. Hu, Z. H. Huang, Q. Zhang, A generalized Newton method for absolute value equations associated with second order cones, J. Comput. Appl. Math., 235 (2011), 1490–1501. https://doi.org/10.1016/j.cam.2010.08.036 doi: 10.1016/j.cam.2010.08.036
    [9] S. Ketabchi, H. Moosaei, An efficient method for optimal correcting of absolute value equations by minimal changes in the right hand side, Comput. Math. Appl., 64 (2012), 1882–1885. https://doi.org/10.1016/j.camwa.2012.03.015 doi: 10.1016/j.camwa.2012.03.015
    [10] C. Zhang, Q. J. Wei, Global and finite convergence of a generalized Newton method for absolute value equations, J. Optim. Theory. Appl., 143 (2009), 391–403. https://doi.org/10.1007/s10957-009-9557-9 doi: 10.1007/s10957-009-9557-9
    [11] J. Rohn, V. Hooshyarbakhsh, R. Farhadsefat, An iterative method for solving absolute value equations and sufficient conditions for unique solvability, Optim. Lett., 8 (2014), 35–44. https://doi.org/10.1007/s11590-012-0560-y doi: 10.1007/s11590-012-0560-y
    [12] Z. Z. Bai, G. H. Golub, M. K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 24 (2003), 603–626. https://doi.org/10.1137/S0895479801395458 doi: 10.1137/S0895479801395458
    [13] M. Z. Zhu, Y. E. Qi, The nonlinear HSS-like iteration method for absolute value equations, IAENG Inter. J. Appl. Math., 48 (2018), 312–316.
    [14] D. K. Salkuyeh, The Picard-HSS iteration method for absolute value equations, Optim. Lett., 8 (2014), 2191–2202. https://doi.org/10.1007/s11590-014-0727-9 doi: 10.1007/s11590-014-0727-9
    [15] J. J. Zhang, The relaxed nonlinear PHSS-like iteration method for absolute value equations, Appl. Math. Comput., 265 (2015), 266–274. https://doi.org/10.1016/j.amc.2015.05.018 doi: 10.1016/j.amc.2015.05.018
    [16] C. X. Li, On the modified Hermitian and skew-Hermitian splitting iteration methods for a class of the weakly absolute value equations, J. Inequal. Appl., 2016 (2016), 260. https://doi.org/10.1186/s13660-016-1202-1 doi: 10.1186/s13660-016-1202-1
    [17] C. X. Li, A preconditioned AOR iterative method for the absolute value equations, Int. J. Comp. Methods, 14 (2017), 1750016. https://doi.org/10.1142/S0219876217500165 doi: 10.1142/S0219876217500165
    [18] X. M. Gu, T. Z. Huang, H. B. Li, S. F. Wang, L. Li, Two CSCS-based iteration methods for solving absolute value equations, J. Appl. Anal. Comput., 7 (2017), 1336–1356. https://doi.org/10.11948/2017082 doi: 10.11948/2017082
    [19] J. He, Y. M. Liu, J. K. Tian, Two numerical iteration methods for solving absolute value equations, ScienceAsia, 44 (2018), 40–45. https://doi.org/10.2306/scienceasia1513-1874.2018.44.040 doi: 10.2306/scienceasia1513-1874.2018.44.040
    [20] Z. S. Yu, L. Li, Y. Yuan, A modified multivariate spectral gradient algorithm for solving absolute value equations, Appl. Math. Lett., 121 (2021), 107461. https://doi.org/10.1016/j.aml.2021.107461 doi: 10.1016/j.aml.2021.107461
    [21] C. R. Chen, Y. N. Yang, D. M. Yu, D. R. Han, An inverse-free dynamical system for solving the absolute value equations, Appl. Numer. Math., 168 (2021), 170–181. https://doi.org/10.1016/j.apnum.2021.06.002 doi: 10.1016/j.apnum.2021.06.002
    [22] Y. F. Ke, C. F. Ma, On SOR-like iteration methods for solving weakly nonlinear systems, Optim. Method. Softw., 2020. https://doi.org/10.1080/10556788.2020.1755861
    [23] Y. F. Ke, The new iteration algorithm for absolute value equation, Appl. Math. Lett., 99 (2020), 105990. https://doi.org/10.1016/j.aml.2019.07.021 doi: 10.1016/j.aml.2019.07.021
    [24] Y. F. Ke, C. F. Ma, SOR-like iteration method for solving absolute value equations, Appl. Math. Comput., 311 (2017), 195–202. https://doi.org/10.1016/j.amc.2017.05.035 doi: 10.1016/j.amc.2017.05.035
    [25] V. Edalatpour, D.Hezari, D. K. Salkuyeh, A generalization of the Gauss-Seidel iteration method for solving absolute value equations, Appl. Math. Comput., 293 (2017), 156–167. https://doi.org/10.1016/j.amc.2016.08.020 doi: 10.1016/j.amc.2016.08.020
    [26] A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic, New York, 1979. https://doi.org/10.1016/C2013-0-10361-3
    [27] R. S. Varga, Matrix Iterative Analysis, Springer, Berlin, 2000. https://doi.org/10.2307/3620826
    [28] S. L. Wu, C. X. Li, Two-sweep modulus-based matrix splitting iteration methods for linear complementarity problems, J. Comput. Appl. Math., 302 (2016), 327–339. https://doi.org/10.1016/j.cam.2016.02.011 doi: 10.1016/j.cam.2016.02.011
    [29] J. L. Dong, M. Q. Jiang, A modified modulus method for symmetric positive-definite linear complementarity problems, Numer. Linear Algebra Appl., 16 (2009), 129–143. https://doi.org/10.1002/nla.609 doi: 10.1002/nla.609
    [30] C. M. Elliot, J. R. Ockenden, Weak Variational Methods for Moving Boundary Value Problems, Pitman, London, 1982. https://doi.org/10.1137/1026023
    [31] Z. Z. Bai, Modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl., 17 (2010), 917–933. https://doi.org/10.1002/nla.680 doi: 10.1002/nla.680
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Electronic Research Archive
1 1.3

Metrics

Article views(1685) PDF downloads(211) Cited by(5)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(7)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog