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A New Finite-Difference Method for Nonlinear Absolute Value Equations

Author

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  • Peng Wang

    (Key Laboratory of Data Science and Smart Education Ministry of Education, Hainan Normal University, Haikou 570203, China
    Key Laboratory of Computational Science and Application of Hainan Province, Haikou 571158, China
    Mathematics and Statistics College, Hainan Normal University, Haikou 570203, China)

  • Yujing Zhang

    (Key Laboratory of Data Science and Smart Education Ministry of Education, Hainan Normal University, Haikou 570203, China
    Key Laboratory of Computational Science and Application of Hainan Province, Haikou 571158, China
    Mathematics and Statistics College, Hainan Normal University, Haikou 570203, China)

  • Detong Zhu

    (Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China)

Abstract

In this paper, we propose a new finite-difference method for nonconvex absolute value equations. The nonsmooth unconstrained optimization problem equivalent to the absolute value equations is considered. The finite-difference technique is considered to compose the linear programming subproblems for obtaining the search direction. The algorithm avoids the computation of gradients and Hessian matrices of problems. The new finite-difference parameter correction technique is considered to ensure the monotonic descent of the objective function. The convergence of the algorithm is analyzed, and numerical experiments are reported, indicating the effectiveness by comparison against a state-of-the-art absolute value equations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:862-:d:1605881
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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. 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.
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