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New Splitting Algorithm with Three Inertial Steps for Three-Operator Monotone Inclusion Problems

Author

Listed:
  • Yonghong Yao

    (Tiangong University
    China Medical University Hospital, China Medical University
    Kyung Hee University)

  • Sani Salisu

    (Sule Lamido University Kafin Hausa)

  • Zai-Yun Peng

    (Yunnan Normal University
    Yunnan Key Laboratory of Modern Analytical Mathematics and Applications)

  • Yekini Shehu

    (Zhejiang Normal University)

Abstract

This paper introduces a new splitting algorithm to solve a three-operator monotone inclusion problem that comprises of the sum of a maximal monotone operator, Lipschitz continuous monotone operator, and a cocoercive operator in real Hilbert spaces. The new splitting algorithm features the following (i) three different inertial extrapolation steps; (ii) one forward evaluation of the Lipschitz continuous monotone operator, one forward evaluation of the cocoercive operator and one backward evaluation of the maximal monotone operator at each iteration. The more interesting feature of the proposed algorithm is that each of the involved operators is evaluated at different inertial step. We establish weak, strong and linear convergence of the sequence of iterates under standard assumptions, respectively. Several known splitting algorithms for the monotone inclusion problems of three-operator sum that have appeared in the literature are considered as special cases of our algorithm. Numerical tests confirm the superiority of our algorithm over related ones in the literature.

Suggested Citation

  • Yonghong Yao & Sani Salisu & Zai-Yun Peng & Yekini Shehu, 2025. "New Splitting Algorithm with Three Inertial Steps for Three-Operator Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-28, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02741-1
    DOI: 10.1007/s10957-025-02741-1
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    References listed on IDEAS

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    1. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    2. Laurent Condat, 2013. "A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 460-479, August.
    3. A. Chambolle & Ch. Dossal, 2015. "On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm”," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 968-982, September.
    4. Puya Latafat & Panagiotis Patrinos, 2017. "Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators," Computational Optimization and Applications, Springer, vol. 68(1), pages 57-93, September.
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