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The global convergence of some self-scaling conjugate gradient methods for monotone nonlinear equations with application to 3DOF arm robot model

Author

Listed:
  • Sulaiman M Ibrahim
  • Lawal Muhammad
  • Rabiu Bashir Yunus
  • Muhammad Yusuf Waziri
  • Saadi bin Ahmad Kamaruddin
  • Aceng Sambas
  • Nooraini Zainuddin
  • Ali F Jameel

Abstract

Conjugate Gradient (CG) methods are widely used for solving large-scale nonlinear systems of equations arising in various real-life applications due to their efficiency in employing vector operations. However, the global convergence analysis of CG methods remains a significant challenge. In response, this study proposes scaled versions of CG parameters based on the renowned Barzilai-Borwein approach for solving convex-constrained monotone nonlinear equations. The proposed algorithms enforce a sufficient descent property independent of the accuracy of the line search procedure and ensure global convergence under appropriate assumptions. Numerical experiments demonstrate the efficiency of the proposed methods in solving large-scale nonlinear systems, including their applicability to accurately solving the inverse kinematic problem of a 3DOF robotic manipulator, where the objective is to minimize the error in achieving a desired trajectory configuration.

Suggested Citation

  • Sulaiman M Ibrahim & Lawal Muhammad & Rabiu Bashir Yunus & Muhammad Yusuf Waziri & Saadi bin Ahmad Kamaruddin & Aceng Sambas & Nooraini Zainuddin & Ali F Jameel, 2025. "The global convergence of some self-scaling conjugate gradient methods for monotone nonlinear equations with application to 3DOF arm robot model," PLOS ONE, Public Library of Science, vol. 20(1), pages 1-36, January.
    • Handle: RePEc:plo:pone00:0317318
    DOI: 10.1371/journal.pone.0317318
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    References listed on IDEAS

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    1. Nasiru Salihu & Poom Kumam & Aliyu Muhammed Awwal & Ibrahim Mohammed Sulaiman & Thidaporn Seangwattana, 2023. "The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-19, March.
    2. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    3. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    4. Gao, Peiting & He, Chuanjiang & Liu, Yang, 2019. "An adaptive family of projection methods for constrained monotone nonlinear equations with applications," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 1-16.
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