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Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results

Author

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  • Yonghong Yao

    (Tiangong University
    Kyung Hee University)

  • Abubakar Adamu

    (Near East University
    African University of Science and Technology)

  • Yekini Shehu

    (Zhejiang Normal University)

Abstract

This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature.

Suggested Citation

  • Yonghong Yao & Abubakar Adamu & Yekini Shehu, 2024. "Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1364-1397, June.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:3:d:10.1007_s10957-024-02410-9
    DOI: 10.1007/s10957-024-02410-9
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    References listed on IDEAS

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    1. 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.
    2. Rieger, Janosch & Tam, Matthew K., 2020. "Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    3. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
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