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An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications

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  • Peeyada, Pronpat
  • Suparatulatorn, Raweerote
  • Cholamjiak, Watcharaporn

Abstract

In this paper, we introduce the inertial Mann forward-backward splitting algorithm for solving variational inclusion problem of the sum of two operators, the one is maximally monotone and the other is monotone and Lipschitz continuous. Under standard assumptions, we prove the weak convergence theorem of the proposed algorithm. We show that the algorithm is flexible to use by choosing the variable stepsizes and two different algorithms are shown by choosing constant stepsize and update stepsize. Moreover, we apply our algorithms to solve data classification using the Wisconsin original breast cancer data set as a training set. We also compare our algorithms with the other two algorithms to show the efficiency of the algorithm and show suitably learns the training dataset and generalizes well to a hold-out dataset of the algorithm by considering overfitting. Finally, we apply our algorithms to solve signal recovery and show the efficiency of the algorithm by compare with the other two algorithms. The results of data classification and signal recovery showed that choosing the right stepsizes of the algorithm would be a good efficient for the different problems.

Suggested Citation

  • Peeyada, Pronpat & Suparatulatorn, Raweerote & Cholamjiak, Watcharaporn, 2022. "An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002582
    DOI: 10.1016/j.chaos.2022.112048
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    References listed on IDEAS

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    1. Haiying Li & Yulian Wu & Fenghui Wang & Xiaolong Qin, 2021. "New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, February.
    2. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
    3. Yonghong Yao & Shin Min Kang & Wu Jigang & Pei-Xia Yang, 2012. "A Regularized Gradient Projection Method for the Minimization Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, February.
    4. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
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    Cited by:

    1. Li-Jun Zhu & Yonghong Yao, 2023. "Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems," Mathematics, MDPI, vol. 11(3), pages 1-12, January.

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