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Superiorization methodology and perturbation resilience of inertial proximal gradient algorithm with application to signal recovery

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Abstract

In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bounded perturbation resilience, we present our proposed algorithm with the superiorization method and apply it to image recovery problem. Finally, we provide the numerical experiments to show efficiency of the proposed algorithm and comparison with previously known algorithms in signal recovery.

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Acknowledgements

This work was completed while the first author, Nuttapol Pakkaranang, was visiting North University Center at Baia Mare, Technical University of Cluj-Napoca on 24 Feburuary–24 May, 2019. He thanks Professor Vasile Berinde for their hospitality and support by ERAMUS+ project and also thanks the Thailand Research Fund (TRF) support through the Royal Golden Jubilee Ph.D. (RGJ-PHD) Program (Grant No. PHD/0205/2561). The second author, Poom Kumam, was supported by the Thailand Research Fund and the King Mongkut’s University of Technology Thonburi (KMUTT) under the TRF Research Scholar (Grant No. RSA6080047). The fourth author, Yusuf I. Suleiman, thanks King Mongkut’s University of Technology Thonburi (KMUTT) for visiting research 6 months (October 2018–March 2019). Furthermore, this project was supported by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT.

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Authors and Affiliations

  1. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Nuttapol Pakkaranang & Poom Kumam

  2. KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Nuttapol Pakkaranang & Poom Kumam

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victorie 76, 430072, Baia-Mare, Romania

    Vasile Berinde

  5. Department of Mathematics, Kano University of Science and Technology, P.M.B. 3042, Wudil, Kano, Nigeria

    Yusuf I. Suleiman

Authors
  1. Nuttapol Pakkaranang
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  2. Poom Kumam
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  3. Vasile Berinde
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  4. Yusuf I. Suleiman
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Corresponding author

Correspondence to Poom Kumam.

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Pakkaranang, N., Kumam, P., Berinde, V. et al. Superiorization methodology and perturbation resilience of inertial proximal gradient algorithm with application to signal recovery. J Supercomput 76, 9456–9477 (2020). https://doi.org/10.1007/s11227-020-03215-z

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