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

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 201; no. 3; pp. 1364 - 1397
Main Authors: Yao, Yonghong, Adamu, Abubakar, Shehu, Yekini
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2024
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Engineering
Hilbert space
Mathematics
Mathematics and Statistics
Momentum
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Splitting
Theory of Computation
68Q25
Monotone inclusion
90C30
Forward–reflected–backward splitting algorithm
68T05
90C25
Weak, linear and strong convergence
Momentum terms
92B20
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02410-9