Self-adaptive forward–backward contraction-type methods for generalized split feasibility problems
Self-adaptive forward–backward contraction-type methods for generalized split feasibility problems
Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.
Generalized split feasibility problems, contraction-type methods, forward–backward algorithms, optimal control sequences, self-adaptive methods
Izuchukwu, Chinedu
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Jolaoso, Lateef Olakunle
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Nnakwe, Monday Ogudu
afa32c80-7e40-4f2d-ac97-7c14d1db272b
Ugwunnadi, Godwin Chidi
437333ca-cb32-46f2-bf49-1c355dd28db3
Khan, Abdul Rahim
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1 October 2022
Izuchukwu, Chinedu
b936c6cb-fac5-4a72-b2b4-e34e7de9628e
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Nnakwe, Monday Ogudu
afa32c80-7e40-4f2d-ac97-7c14d1db272b
Ugwunnadi, Godwin Chidi
437333ca-cb32-46f2-bf49-1c355dd28db3
Khan, Abdul Rahim
adf5b9c9-e0ef-4a8d-8f55-76bf72f2d3d9
Izuchukwu, Chinedu, Jolaoso, Lateef Olakunle, Nnakwe, Monday Ogudu, Ugwunnadi, Godwin Chidi and Khan, Abdul Rahim
(2022)
Self-adaptive forward–backward contraction-type methods for generalized split feasibility problems.
Mediterranean Journal of Mathematics, 19 (5), [204].
(doi:10.1007/s00009-022-02114-2).
Abstract
Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.
Text
2206.04366
- Accepted Manuscript
More information
Accepted/In Press date: 3 August 2022
e-pub ahead of print date: 29 August 2022
Published date: 1 October 2022
Additional Information:
Funding Information:
The authors thank the reviewer for the time spent and efforts made to read through the manuscript and for his/her constructive comments, questions and suggestions, which have helped to improve the quality of the article.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Keywords:
Generalized split feasibility problems, contraction-type methods, forward–backward algorithms, optimal control sequences, self-adaptive methods
Identifiers
Local EPrints ID: 471562
URI: http://eprints.soton.ac.uk/id/eprint/471562
ISSN: 1660-5446
PURE UUID: 59c04fbe-fb41-4416-92a3-18abd650acfd
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Date deposited: 11 Nov 2022 17:34
Last modified: 17 Mar 2024 07:33
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Contributors
Author:
Chinedu Izuchukwu
Author:
Monday Ogudu Nnakwe
Author:
Godwin Chidi Ugwunnadi
Author:
Abdul Rahim Khan
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