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Some techniques for solving absolute value equations

Author

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  • Moosaei, H.
  • Ketabchi, S.
  • Noor, M.A.
  • Iqbal, J.
  • Hooshyarbakhsh, V.

Abstract

In this paper, we introduce and analyze two new methods for solving the NP-hard absolute value equations (AVE) Ax−|x|=b, where A is an arbitrary n × n real matrix and b ∈ Rn, in the case, singular value of A exceeds 1. The comparison with other known methods is carried to show the effectiveness of the proposed methods for a variety of randomly generated problems. The ideas and techniques of this paper may stimulate further research.

Suggested Citation

  • Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:696-705
    DOI: 10.1016/j.amc.2015.06.072
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    References listed on IDEAS

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    1. C. Kanzow & H. Qi & L. Qi, 2003. "On the Minimum Norm Solution of Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 333-345, February.
    2. C. Zhang & Q. J. Wei, 2009. "Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 391-403, November.
    3. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
    5. Keramati, B., 2009. "An approach to the solution of linear system of equations by He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 152-156.
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    Cited by:

    1. Milan Hladík, 2018. "Bounds for the solutions of absolute value equations," Computational Optimization and Applications, Springer, vol. 69(1), pages 243-266, January.
    2. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    3. Ke, Yi-Fen & Ma, Chang-Feng, 2017. "SOR-like iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 195-202.
    4. Peng Wang & Yujing Zhang & Detong Zhu, 2025. "A New Finite-Difference Method for Nonlinear Absolute Value Equations," Mathematics, MDPI, vol. 13(5), pages 1-12, March.
    5. Milan Hladík & Hossein Moosaei & Fakhrodin Hashemi & Saeed Ketabchi & Panos M. Pardalos, 2026. "An overview of absolute value equations: from theory to solution methods and challenges," Computational Optimization and Applications, Springer, vol. 93(1), pages 435-488, January.
    6. Hossein Moosaei & Saeed Ketabchi & Milan Hladík, 2021. "Optimal correction of the absolute value equations," Journal of Global Optimization, Springer, vol. 79(3), pages 645-667, March.

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