Four-operator reflected forward-backward algorithm for solving monotone inclusions involving Lipschitzian operator

In this work, using a discretisation of continuous-time dynamical systems, we design a novel splitting algorithm without the lifting technique for finding the sum of three maximal monotone operators and a monotone operator with Lipschitz continuity. In theory, we analyze the weak and strong converge...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 153; p. 109485
Main Authors: Cao, Yu, Wang, Yuanheng, Ur Rehman, Habib, Shehu, Yekini, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2026
Subjects:
Forward-backward splitting algorithm
Lipschitz continuous
Maximal monotone
Reflected technique
68Q25
Forward-backward splitting algorithm
Maximal monotone
90C25
Lipschitz continuous
47H05
49M25
Reflected technique
ISSN:1007-5704
Online Access:Get full text
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Summary:In this work, using a discretisation of continuous-time dynamical systems, we design a novel splitting algorithm without the lifting technique for finding the sum of three maximal monotone operators and a monotone operator with Lipschitz continuity. In theory, we analyze the weak and strong convergence of the proposed splitting algorithm and show the sublinear convergence rate. The practical efficacy of the proposed algorithm is validated through image restoration experiments, where it outperforms existing methods.
ISSN:1007-5704
DOI:10.1016/j.cnsns.2025.109485