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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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 12; pp. 28398 - 28412
Main Author Artsawang, Natthaphon
Format Journal Article
LanguageEnglish
Published AIMS Press 2023
Subjects
fixed point problem
krasnosel'skiĭ-mann method
minimizaton problem
monotone inclusion problem
nonexpansive mapping
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231453