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Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity

Author

Listed:
  • Yu Cao

    (Zhejiang Normal University)

  • Yuanheng Wang

    (Zhejiang Normal University)

  • Habib Rehman

    (Zhejiang Normal University)

  • Yekini Shehu

    (Zhejiang Normal University)

  • Jen-Chih Yao

    (China Medical University
    Academy of Romanian Scientists)

Abstract

In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the sequence of iterates generated by our proposed splitting algorithm converges weakly to the zero of the considered inclusion problem under mild conditions on the iterative parameters. Several splitting algorithms in the literature are recovered as special cases of our proposed algorithm. Another interesting feature of our algorithm is that one forward evaluation of the Lipschitz continuous monotone operator is utilized at each iteration. Numerical results are given to support the theoretical analysis.

Suggested Citation

  • Yu Cao & Yuanheng Wang & Habib Rehman & Yekini Shehu & Jen-Chih Yao, 2024. "Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 256-284, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02501-7
    DOI: 10.1007/s10957-024-02501-7
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