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Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems

Author

Listed:
  • Yuanheng Wang

    (College of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Miaoqing Li

    (College of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Chengru Yao

    (Xichuan County Education and Sports Bureau of Henan Province, Nanyang 474450, China)

  • Bingnan Jiang

    (College of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

Abstract

In this article, based on the regularization techniques, we construct two new algorithms combining the forward-backward splitting algorithm and the proximal contraction algorithm, respectively. Iterative sequences of the new algorithms can converge strongly to a common solution of the variational inclusion and null point problems in real Hilbert spaces. Multi-inertial extrapolation steps are applied to expedite their convergence rate. We also give some numerical experiments to certify that our algorithms are viable and efficient.

Suggested Citation

  • Yuanheng Wang & Miaoqing Li & Chengru Yao & Bingnan Jiang, 2023. "Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1469-:d:1100360
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    References listed on IDEAS

    as
    1. Yanlai Song & Omar Bazighifan, 2022. "Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    2. Bingnan Jiang & Yuanheng Wang & Jen-Chih Yao, 2021. "Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings," Mathematics, MDPI, vol. 9(17), pages 1-20, August.
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