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Convergence-Accelerated Fixed-Time Dynamical Methods for Absolute Value Equations

Author

Listed:
  • Xu Zhang

    (Xiangtan University
    The Key Laboratory of Credible Intelligent Navigation and Positioning of Hunan)

  • Cailian Li

    (Xiangtan University)

  • Longcheng Zhang

    (Xiangtan University)

  • Yaling Hu

    (Xiangtan University)

  • Zheng Peng

    (Xiangtan University)

Abstract

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): $$Ax-|x|-b=0$$ A x - | x | - b = 0 . Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution of the AVEs under consideration. Meanwhile, we have introduced a new relatively tighter global error bound for the AVEs. Leveraging this finding, we have separately established the globally fixed-time stability of the proposed methods, along with providing the conservative settling-time for each method. Compared with some existing state-of-the-art dynamical methods, preliminary numerical experiments show the effectiveness of our methods in solving the AVEs.

Suggested Citation

  • Xu Zhang & Cailian Li & Longcheng Zhang & Yaling Hu & Zheng Peng, 2024. "Convergence-Accelerated Fixed-Time Dynamical Methods for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 600-628, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02525-z
    DOI: 10.1007/s10957-024-02525-z
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    References listed on IDEAS

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    1. N. H. Xiu & J. Z. Zhang, 2002. "Global Projection-Type Error Bounds for General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 213-228, January.
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    4. 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.
    5. Saeed Ketabchi & Hossein Moosaei, 2012. "Minimum Norm Solution to the Absolute Value Equation in the Convex Case," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 1080-1087, September.
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