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Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations

Author

Listed:
  • An Wang

    (Nantong University)

  • Yang Cao

    (Nantong University)

  • Jing-Xian Chen

    (Nantong University)

Abstract

In this paper, by separating the differential and the non-differential parts of the generalized absolute value equations, a class of modified Newton-type iteration methods are proposed. The modified Newton-type iteration method involves the well-known Picard iteration method as the special case. Convergence properties of the new iteration schemes are analyzed in detail. In particular, some specific sufficient conditions are presented for two special coefficient matrices. Finally, two numerical examples are given to illustrate the effectiveness of the proposed modified Newton-type iteration methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1439-6
    DOI: 10.1007/s10957-018-1439-6
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    References listed on IDEAS

    as
    1. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
    2. 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.
    3. 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.
    4. Farhad Khaksar Haghani, 2015. "On Generalized Traub’s Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 619-625, August.
    5. Shi-Liang Wu & Peng Guo, 2016. "On the Unique Solvability of the Absolute Value Equation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 705-712, May.
    6. 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.
    7. Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
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    Cited by:

    1. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.

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