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

Natthaphon Artsawang; Natthaphon Artsawang

doi:10.3934/math.20231453

AIMS Mathematics

2023, Volume 8, Issue 12: 28398-28412. doi: 10.3934/math.20231453

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Research article

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

Natthaphon Artsawang ^{1,2
,
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1.
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2.
Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received: 22 August 2023 Revised: 22 September 2023 Accepted: 11 October 2023 Published: 18 October 2023
MSC : 47H04, 47H10, 65K05, 90C25

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.
- Krasnosel'skiĭ-Mann method,
- nonexpansive mapping,
- monotone inclusion problem,
- fixed point problem,
- minimizaton problem
Citation: Natthaphon Artsawang. Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems[J]. AIMS Mathematics, 2023, 8(12): 28398-28412. doi: 10.3934/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.

References

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