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Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring

Author

Listed:
  • Branislav Ivanov

    (University of Belgrade)

  • Gradimir V. Milovanović

    (Serbian Academy of Sciences and Arts
    University of Niš)

  • Predrag S. Stanimirović

    (University of Niš)

Abstract

A modified Dai-Liao type conjugate gradient method for solving large-scale nonlinear systems of monotone equations is introduced and investigated in actual research. The starting point is the Dai-Liao type conjugate gradient method which is based on the descent Dai-Liao method and the hyperplane projection technique, known as the Dai-Liao projection method (DLPM). Our algorithm, termed MSMDLPM, proposes a novel search direction for the DLPM, which arises from appropriate acceleration parameters obtained after hybridizing the accelerated gradient-descent method MSM with the DLPM method. The main goal of the proposed MSMDLPM method is to correlate the MSM and the DLPM. The global convergence and the convergence rate of the MSMDLPM method are investigated theoretically. Numerical results show the efficiency of the proposed method in solving large-scale nonlinear systems of monotone equations. The effectiveness of the method in image restoration is verified based on performed numerical experiments.

Suggested Citation

  • Branislav Ivanov & Gradimir V. Milovanović & Predrag S. Stanimirović, 2023. "Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring," Journal of Global Optimization, Springer, vol. 85(2), pages 377-420, February.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:2:d:10.1007_s10898-022-01213-4
    DOI: 10.1007/s10898-022-01213-4
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    References listed on IDEAS

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    1. Zohre Aminifard & Saman Babaie-Kafaki, 2019. "An optimal parameter choice for the Dai–Liao family of conjugate gradient methods by avoiding a direction of the maximum magnification by the search direction matrix," 4OR, Springer, vol. 17(3), pages 317-330, September.
    2. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    3. Babaie-Kafaki, Saman & Ghanbari, Reza, 2014. "The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices," European Journal of Operational Research, Elsevier, vol. 234(3), pages 625-630.
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