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An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems

Author

Listed:
  • Huan Zhang

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Xiaolan Liu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China
    Artificial Intelligence Key Laboratory of Sichuan Province, Zigong 643000, China)

  • Yan Sun

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Ju Hu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

Abstract

In this paper, we propose an alternated inertial projection algorithm for solving multi-valued variational inequality problem and fixed point problem of demi-contractive mapping. On one hand, this algorithm only requires the mapping is pseudo-monotone. On the other hand, this algorithm is combined with the alternated inertial method to accelerate the convergence speed. The global convergence of the algorithm can be obtained under mild conditions. Preliminary numerical results show that the convergence speed of our algorithm is faster than some existing algorithms.

Suggested Citation

  • Huan Zhang & Xiaolan Liu & Yan Sun & Ju Hu, 2023. "An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1850-:d:1122657
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    References listed on IDEAS

    as
    1. Yonghong Yao & Mihai Postolache, 2012. "Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 273-287, October.
    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. Franck Iutzeler & Jérôme Malick, 2018. "On the Proximal Gradient Algorithm with Alternated Inertia," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 688-710, March.
    4. Jolaoso, Lateef O. & Shehu, Yekini & Yao, Jen-Chih, 2022. "Inertial extragradient type method for mixed variational inequalities without monotonicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 353-369.
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