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

Yonghong Yao (), Abubakar Adamu () and Yekini Shehu ()
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Yonghong Yao: Tiangong University
Abubakar Adamu: Near East University
Yekini Shehu: Zhejiang Normal University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 3, No 16, 1364-1397

Abstract: 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.

Keywords: Forward–reflected–backward splitting algorithm; Monotone inclusion; Momentum terms; Weak; linear and strong convergence; 68Q25; 68T05; 92B20; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02410-9

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