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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
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Research Article

Strong convergence of inertial forward–backward methods for solving monotone inclusions

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Pages 5386-5414 | Received 02 Oct 2020, Accepted 12 Feb 2021, Published online: 25 Feb 2021
 

ABSTRACT

The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.

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Acknowledgements

The authors are very grateful to the anonymous referees for their constructive comments, which significantly improved the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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