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A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Author

Listed:
  • Zhifeng Dai

    (College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China)

  • Huan Zhu

    (College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China)

Abstract

The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F. A globally convergent inexact Newton method for systems of monotone equations, in: M. Fukushima, L. Qi (Eds.)Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers. 1998, 355-369) and the modified Hestenes-Stiefel method in Dai and Wen (Dai, Z.; Wen, F. Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. Numer Algor. 2012, 59, 79-93). In addition, we propose a new line search for the derivative-free method. Global convergence of the proposed method is established if the system of nonlinear equations are Lipschitz continuous and monotone. Preliminary numerical results are given to test the effectiveness of the proposed method.

Suggested Citation

  • Zhifeng Dai & Huan Zhu, 2020. "A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations," Mathematics, MDPI, vol. 8(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:168-:d:314562
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    References listed on IDEAS

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    1. Yilun Shang, 2019. "Super Connectivity of Erdős-Rényi Graphs," Mathematics, MDPI, vol. 7(3), pages 1-5, March.
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    Cited by:

    1. Eltiyeb Ali & Salem Mahdi, 2023. "Adaptive Hybrid Mixed Two-Point Step Size Gradient Algorithm for Solving Non-Linear Systems," Mathematics, MDPI, vol. 11(9), pages 1-35, April.
    2. Dai, Zhifeng & Luo, Zhuang & Liu, Chang, 2023. "Dynamic volatility spillovers and investment strategies between crude oil, new energy, and resource related sectors," Resources Policy, Elsevier, vol. 83(C).
    3. Dai, Zhifeng & Tang, Rui & Zhang, Xiaotong, 2023. "A new multilayer network for measuring interconnectedness among the energy firms," Energy Economics, Elsevier, vol. 124(C).

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