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An efficient Newton-like conjugate gradient method with restart strategy and its application

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  • Salihu, Nasiru
  • Kumam, Poom
  • Sulaiman, Ibrahim Mohammed
  • Arzuka, Ibrahim
  • Kumam, Wiyada

Abstract

In an attempt to enhance the theoretical structure of the Hestenes and Stiefel (HS) conjugate gradient method, several modifications of the method are provided, most of which rely on a double-truncated property to analyze its convergence properties. In this paper, a spectral HS method is proposed, which is sufficiently descent and converges globally using Powell’s restart strategy. This modification makes it possible to relax the double bounded property associated with the earlier versions of the HS method. Furthermore, the spectral parameter is motivated by some interesting theoretical features of the generalized conjugacy condition, as well as the quadratic convergence property of the Newton method. Based on some standard test problems, the numerical results reveal the advantages of the method compared to some popular conjugate gradient methods. Additionally, the method also demonstrates reliable results when applied to solve image reconstruction models.

Suggested Citation

  • Salihu, Nasiru & Kumam, Poom & Sulaiman, Ibrahim Mohammed & Arzuka, Ibrahim & Kumam, Wiyada, 2024. "An efficient Newton-like conjugate gradient method with restart strategy and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 354-372.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:354-372
    DOI: 10.1016/j.matcom.2024.07.008
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    References listed on IDEAS

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    1. Parvaneh Faramarzi & Keyvan Amini, 2019. "A Modified Spectral Conjugate Gradient Method with Global Convergence," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 667-690, August.
    2. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.
    3. Parvaneh Faramarzi & Keyvan Amini, 2021. "A spectral three-term Hestenes–Stiefel conjugate gradient method," 4OR, Springer, vol. 19(1), pages 71-92, March.
    4. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, December.
    5. 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.
    6. 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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