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An Accelerated Diagonally Structured CG Algorithm for Nonlinear Least Squares and Inverse Kinematics

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  • Rabiu Bashir Yunus

    (Department of Applied Science, Faculty of Science, Management & Computing, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
    Department of Mathematics, Faculty of Computing and Mathematical Sciences, Aliko Dangote University of Science and Technology, Wudil 713101, Kano, Nigeria)

  • Anis Ben Ghorbal

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Nooraini Zainuddin

    (Department of Applied Science, Faculty of Science, Management & Computing, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia)

  • Sulaiman Mohammed Ibrahim

    (School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok 06010, Kedah, Malaysia
    Faculty of Education and Arts, Sohar University, Sohar 311, Oman)

Abstract

Nonlinear least squares (NLS) models are extensively used as optimization frameworks in various scientific and engineering disciplines. This work proposes a novel structured conjugate gradient (SCG) method that incorporates a structured diagonal approximation for the second-order term of the Hessian, particularly designed for solving NLS problems. In addition, an acceleration scheme for the SCG method is proposed and analyzed. The global convergence properties of the proposed method are rigorously established under specific assumptions. Numerical experiments were conducted on large-scale NLS benchmark problems to evaluate the performance of the method. The outcome of these experiments indicates that the proposed method outperforms other approaches using the established performance metrics. Moreover, the developed approach is utilized to address the inverse kinematics challenge in controlling the motion of a robotic system with four degrees of freedom (4DOF).

Suggested Citation

  • Rabiu Bashir Yunus & Anis Ben Ghorbal & Nooraini Zainuddin & Sulaiman Mohammed Ibrahim, 2025. "An Accelerated Diagonally Structured CG Algorithm for Nonlinear Least Squares and Inverse Kinematics," Mathematics, MDPI, vol. 13(17), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2766-:d:1736059
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