Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems

In this article, we propose a strongly convergent preconditioning method for finding a zero of the sum of two monotone operators. The proposed method combines a preconditioning approach with the robustness of the Krasnosel'skiĭ-Mann method. We show the strong convergence result of the sequence...

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Published inAIMS mathematics Vol. 8; no. 12; pp. 28398 - 28412
Main Author Artsawang, Natthaphon
Format Journal Article
LanguageEnglish
Published AIMS Press 01.10.2023
Subjects
fixed point problem
krasnosel'skiĭ-mann method
minimizaton problem
monotone inclusion problem
nonexpansive mapping
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ISSN2473-6988
2473-6988
DOI10.3934/math.20231453

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Abstract In this article, we propose a strongly convergent preconditioning method for finding a zero of the sum of two monotone operators. The proposed method combines a preconditioning approach with the robustness of the Krasnosel'skiĭ-Mann method. We show the strong convergence result of the sequence generated by the proposed method to a solution of the monotone inclusion problem. Finally, we provide numerical experiments on the convex minimization problem.
AbstractList In this article, we propose a strongly convergent preconditioning method for finding a zero of the sum of two monotone operators. The proposed method combines a preconditioning approach with the robustness of the Krasnosel'skiĭ-Mann method. We show the strong convergence result of the sequence generated by the proposed method to a solution of the monotone inclusion problem. Finally, we provide numerical experiments on the convex minimization problem.
Author Artsawang, Natthaphon
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  organization: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand, Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
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SubjectTerms fixed point problem
krasnosel'skiĭ-mann method
minimizaton problem
monotone inclusion problem
nonexpansive mapping
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Title Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems
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