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On the global convergence of the inexact semi-smooth Newton method for absolute value equation

Author

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  • J. Y. Bello Cruz

    (IME/UFG)

  • O. P. Ferreira

    (IME/UFG)

  • L. F. Prudente

    (IME/UFG)

Abstract

In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations. Global Q-linear convergence is established under suitable assumptions. Moreover, we present some numerical experiments designed to investigate the practical viability of the proposed scheme.

Suggested Citation

  • J. Y. Bello Cruz & O. P. Ferreira & L. F. Prudente, 2016. "On the global convergence of the inexact semi-smooth Newton method for absolute value equation," Computational Optimization and Applications, Springer, vol. 65(1), pages 93-108, September.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:1:d:10.1007_s10589-016-9837-x
    DOI: 10.1007/s10589-016-9837-x
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    References listed on IDEAS

    as
    1. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    2. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
    3. 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.
    4. Olvi L. Mangasarian, 2014. "Absolute Value Equation Solution Via Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 870-876, June.
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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. Juan Yin & Qingna Li, 2019. "A semismooth Newton method for support vector classification and regression," Computational Optimization and Applications, Springer, vol. 73(2), pages 477-508, June.
    3. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    4. 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.
    5. Butyn, Emerson & Karas, Elizabeth W. & de Oliveira, Welington, 2022. "A derivative-free trust-region algorithm with copula-based models for probability maximization problems," European Journal of Operational Research, Elsevier, vol. 298(1), pages 59-75.
    6. Fabiana R. Oliveira & Fabrícia R. Oliveira, 2021. "A Global Newton Method for the Nonsmooth Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 259-273, July.
    7. An Wang & Yang Cao & Jing-Xian Chen, 2019. "Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 216-230, April.

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