Three-operator reflected forward-backward splitting algorithm with double inertial effects

In this paper, we propose a reflected forward-backward splitting algorithm with two different inertial extrapolations to find a zero of the sum of three monotone operators consisting of the maximal monotone operator, Lipschitz continuous monotone operator, and a cocoercive operator in real Hilbert s...

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Bibliographic Details
Published in:	Optimization methods & software Vol. 39; no. 2; pp. 431 - 456
Main Authors:	Dong, Qiao-Li, Su, Min, Shehu, Yekini
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 03.03.2024 Taylor & Francis Ltd
Subjects:	Algorithms Hilbert space inertial extrapolation step Operators (mathematics) Splitting Three-operator splitting algorithm weak and strong convergence
ISSN:	1055-6788, 1029-4937
Online Access:	Get full text
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Summary:	In this paper, we propose a reflected forward-backward splitting algorithm with two different inertial extrapolations to find a zero of the sum of three monotone operators consisting of the maximal monotone operator, Lipschitz continuous monotone operator, and a cocoercive operator in real Hilbert spaces. One of the interesting features of the proposed algorithm is that both the Lipschitz continuous monotone operator and the cocoercive operator are computed explicitly each with one evaluation per iteration. We then obtain weak and strong convergence results under some mild conditions. We finally give a numerical illustration to show that our proposed algorithm is effective and competitive with other related algorithms in the literature.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1055-6788 1029-4937
DOI:	10.1080/10556788.2024.2307470