Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems-Reference-Cited by-同舟云学术

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

Published:2023 Issue:12 Volume:8 Page:28398-28412
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Artsawang Natthaphon¹²

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference34 articles.

1. H. H. Bauschke, P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, New York: Springer Cham, 2011. https://doi.org/10.1007/978-3-319-48311-5

2. B. Engquist, Encyclopedia of applied and computational mathematics, Berlin: Springer, 2015. https://doi.org/10.1007/978-3-540-70529-1

3. J. Eckstein, D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program., 55 (1992), 293–318. https://doi.org/10.1007/BF01581204

4. N. Artsawang, K. Ungchittrakool, A new forward-backward penalty scheme and its convergence for solving monotone inclusion problems, Carpathian. J. Math., 35 (2019), 349–363.

5. N. Artsawang, K. Ungchittrakool, A new splitting forward-backward algorithm and convergence for solving constrained convex optimization problem in Hilbert spaces, J. Nonlinear Convex Anal., 22 (2021), 1003–1023.

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