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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Vydáno v:Communications in nonlinear science & numerical simulation Ročník 153; s. 109485
Hlavní autoři: Cao, Yu, Wang, Yuanheng, Ur Rehman, Habib, Shehu, Yekini, Yao, Jen-Chih
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.02.2026
Témata:
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
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Popis
Shrnutí: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