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A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems

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  • Abubakar, Auwal Bala
  • Kumam, Poom
  • Malik, Maulana
  • Ibrahim, Abdulkarim Hassan

Abstract

In this article, we propose a hybrid conjugate gradient (CG) scheme for solving unconstrained optimization problem. The search direction is a combination of the Polak–Ribière–Polyak (PRP) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton scheme. Without the use of the line search, the search direction satisfies the descent condition and possesses the trust region property. The global convergence of the scheme for general functions under the Wolfe-type and Armijo-type line search is established. Numerical experiments are carried out on some benchmark test problems and the results show that the propose scheme is more efficient than other existing schemes. Finally, a practical application of the scheme in motion control of robot manipulator is also presented.

Suggested Citation

  • Abubakar, Auwal Bala & Kumam, Poom & Malik, Maulana & Ibrahim, Abdulkarim Hassan, 2022. "A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 640-657.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:640-657
    DOI: 10.1016/j.matcom.2021.05.038
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    References listed on IDEAS

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    1. David F. Shanno, 1978. "Conjugate Gradient Methods with Inexact Searches," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 244-256, August.
    2. Zexian Liu & Hongwei Liu & Yu-Hong Dai, 2020. "An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 75(1), pages 145-167, January.
    3. Min Sun & Jing Liu & Yaru Wang, 2020. "Two Improved Conjugate Gradient Methods with Application in Compressive Sensing and Motion Control," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, May.
    4. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, September.
    5. Neculai Andrei, 2020. "General Convergence Results for Nonlinear Conjugate Gradient Methods," Springer Optimization and Its Applications, in: Nonlinear Conjugate Gradient Methods for Unconstrained Optimization, chapter 0, pages 89-123, Springer.
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    Cited by:

    1. Mrad, Hatem & Fakhari, Seyyed Mojtaba, 2024. "Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 282-290.
    2. Jing, Shaoxue, 2023. "Time-delay Hammerstein system identification using modified cross-correlation method and variable stacking length multi-error algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 288-300.

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