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A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Author

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  • Suthep Suantai

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Pronpat Peeyada

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Damrongsak Yambangwai

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Watcharaporn Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

Suggested Citation

  • Suthep Suantai & Pronpat Peeyada & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2020. "A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:248-:d:320543
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    References listed on IDEAS

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    1. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
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    Cited by:

    1. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2024. "Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems," Networks and Spatial Economics, Springer, vol. 24(2), pages 425-459, June.
    2. Cholamjiak, Watcharaporn & Dutta, Hemen & Yambangwai, Damrongsak, 2021. "Image restorations using an inertial parallel hybrid algorithm with Armijo linesearch for nonmonotone equilibrium problems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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