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Image restorations using an inertial parallel hybrid algorithm with Armijo linesearch for nonmonotone equilibrium problems

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  • Cholamjiak, Watcharaporn
  • Dutta, Hemen
  • Yambangwai, Damrongsak

Abstract

In this work, we modify the inertial type parallel monotone hybrid algorithm with Armijo linesearch to solve common nonmonotone equilibrium problems. The weak convergence theorem is established under some suitable conditions in Hilbert spaces. Finally, the numerical example is shown to support our main result. The efficiencies of the proposed algorithm are presented by comparing with previously parallel algorithms in novel image restoration. It’s illustrated that the proposed algorithm can increase deblurring quality when the subproblems are increasing.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s096007792100816x
    DOI: 10.1016/j.chaos.2021.111462
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    References listed on IDEAS

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    1. Phan Tu Vuong & Jean Jacques Strodiot & Van Hien Nguyen, 2012. "Extragradient Methods and Linesearch Algorithms for Solving Ky Fan Inequalities and Fixed Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 605-627, November.
    2. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    3. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    4. 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.
    5. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    6. Tran Quoc & Pham Anh & Le Muu, 2012. "Dual extragradient algorithms extended to equilibrium problems," Journal of Global Optimization, Springer, vol. 52(1), pages 139-159, January.
    7. Hongjin He & Chen Ling & Hong-Kun Xu, 2015. "A Relaxed Projection Method for Split Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 213-233, July.
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    Cited by:

    1. Sining Huang & Yupeng Chen & Tiantian Qiao, 2021. "An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration," Mathematics, MDPI, vol. 9(24), pages 1-15, December.

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