Inertial projection and contraction methods for solving variational inequalities with applications to image restoration problems
Inertial projection and contraction methods for solving variational inequalities with applications to image restoration problems
In this paper, we introduce two inertial self-adaptive projection and contraction methods for solving the pseudomonotone variational inequality problem with a Lipschitz-continuous mapping in real Hilbert spaces. The adaptive stepsizes provided by the algorithms are simple to update and their computations are more efficient and flexible. Also we prove some weak and strong convergence theorems without prior knowledge of the Lipschitz constant of the mapping. Finally, we present some numerical experiments to demonstrate the effectiveness of the proposed algorithms by comparisons with related methods and some applications of the proposed algorithms to the image deblurring problem.
Hilbert space, Projection and contraction method, Pseudomonotone mapping, Variational inequality problem
683-704
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Sunthrayuth, Pongsakorn
3f5f8302-db73-41fa-9caf-5ed1782d41be
Cholamjiak, Prasit
ca478763-4dff-4e84-b521-ec266b1cfc47
Cho, Yeol Je
40712d53-5d15-4433-87ca-12381c8d1115
2023
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Sunthrayuth, Pongsakorn
3f5f8302-db73-41fa-9caf-5ed1782d41be
Cholamjiak, Prasit
ca478763-4dff-4e84-b521-ec266b1cfc47
Cho, Yeol Je
40712d53-5d15-4433-87ca-12381c8d1115
Jolaoso, Lateef Olakunle, Sunthrayuth, Pongsakorn, Cholamjiak, Prasit and Cho, Yeol Je
(2023)
Inertial projection and contraction methods for solving variational inequalities with applications to image restoration problems.
Carpathian Journal of Mathematics, 39 (3), .
Abstract
In this paper, we introduce two inertial self-adaptive projection and contraction methods for solving the pseudomonotone variational inequality problem with a Lipschitz-continuous mapping in real Hilbert spaces. The adaptive stepsizes provided by the algorithms are simple to update and their computations are more efficient and flexible. Also we prove some weak and strong convergence theorems without prior knowledge of the Lipschitz constant of the mapping. Finally, we present some numerical experiments to demonstrate the effectiveness of the proposed algorithms by comparisons with related methods and some applications of the proposed algorithms to the image deblurring problem.
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Accepted/In Press date: 18 February 2023
Published date: 2023
Additional Information:
Funding Information:
P. Cholamjiak was supported by University of Phayao and Thailand Science Research and Innovation grant no. FF66-UoE and Y. J. Cho thanks Thailand Science Research and Innovation (IRN62W0007). This research was supported by The Science, Research and Innovation Promotion Funding (TSRI) (Grant no. FRB660012/0168). This research block grants was managed under Rajamangala University of Technology Thanyaburi (FRB66E0628).
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Keywords:
Hilbert space, Projection and contraction method, Pseudomonotone mapping, Variational inequality problem
Identifiers
Local EPrints ID: 484139
URI: http://eprints.soton.ac.uk/id/eprint/484139
ISSN: 1584-2851
PURE UUID: 31b42d07-317f-47de-88f8-ee11048ebee6
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Date deposited: 10 Nov 2023 18:03
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
Pongsakorn Sunthrayuth
Author:
Prasit Cholamjiak
Author:
Yeol Je Cho
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