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Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Author

Listed:
  • Suthep Suantai

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Suparat Kesornprom

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

  • Prasit Cholamjiak

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

Abstract

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

Suggested Citation

  • Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:708-:d:255273
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    References listed on IDEAS

    as
    1. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    2. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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    Cited by:

    1. Panadda Thongpaen & Rattanakorn Wattanataweekul, 2021. "A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    2. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    3. Kobkoon Janngam & Suthep Suantai, 2022. "An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems," Mathematics, MDPI, vol. 10(23), pages 1-15, November.
    4. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.

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