Inertial-like Bregman projection method for solving systems of variational inequalities
Inertial-like Bregman projection method for solving systems of variational inequalities
In this paper, we propose a self-adaptive inertial-like algorithm with Bregman distance for approximating a common solution of systems of variational inequalities for a class of monotone and Lipschitz continuous mappings in real reflexive Banach spaces. Our algorithm is constructed without using hybrid projection method and shrinking projection method, and its strong convergence is proved without the prior information of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to illustrate the performance of the newly proposed method including a comparison with related works in solving signal restoration problems.
Bregman distance, monotone mapping, reflexive Banach space, strong convergence, variational inequality problem
16876-16898
Olakunle Jolaoso, Lateef
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Pholasa, Nattawut
366b05f0-11a8-4022-9f3e-b3d9008ead0b
Sunthrayuth, Pongsakorn
3f5f8302-db73-41fa-9caf-5ed1782d41be
Cholamjiak, Prasit
ca478763-4dff-4e84-b521-ec266b1cfc47
15 November 2023
Olakunle Jolaoso, Lateef
102467df-eae0-4692-8668-7f73e8e02546
Pholasa, Nattawut
366b05f0-11a8-4022-9f3e-b3d9008ead0b
Sunthrayuth, Pongsakorn
3f5f8302-db73-41fa-9caf-5ed1782d41be
Cholamjiak, Prasit
ca478763-4dff-4e84-b521-ec266b1cfc47
Olakunle Jolaoso, Lateef, Pholasa, Nattawut, Sunthrayuth, Pongsakorn and Cholamjiak, Prasit
(2023)
Inertial-like Bregman projection method for solving systems of variational inequalities.
Mathematical Methods in the Applied Sciences, 46 (16), .
(doi:10.1002/mma.9479).
Abstract
In this paper, we propose a self-adaptive inertial-like algorithm with Bregman distance for approximating a common solution of systems of variational inequalities for a class of monotone and Lipschitz continuous mappings in real reflexive Banach spaces. Our algorithm is constructed without using hybrid projection method and shrinking projection method, and its strong convergence is proved without the prior information of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to illustrate the performance of the newly proposed method including a comparison with related works in solving signal restoration problems.
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Accepted/In Press date: 5 June 2023
e-pub ahead of print date: 24 June 2023
Published date: 15 November 2023
Additional Information:
Funding Information:
This research was supported by The Science, Research and Innovation Promotion Funding (TSRI) (grant no. FRB660012/0168). This research block grant was managed under Rajamangala University of Technology Thanyaburi (FRB66E0628). P. Cholamjiak was supported by the University of Phayao and Thailand Science Research and Innovation grant no. FF66‐UoE. The authors would like to thank the editor and the anonymous reviewers for their helpful and constructive comments to improve the quality of this manuscript.
Publisher Copyright:
© 2023 John Wiley & Sons, Ltd.
Keywords:
Bregman distance, monotone mapping, reflexive Banach space, strong convergence, variational inequality problem
Identifiers
Local EPrints ID: 479836
URI: http://eprints.soton.ac.uk/id/eprint/479836
ISSN: 0170-4214
PURE UUID: ac30d979-bebc-47a8-9bb3-f5c833d76fc7
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Date deposited: 27 Jul 2023 15:01
Last modified: 24 Jun 2024 04:01
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Contributors
Author:
Nattawut Pholasa
Author:
Pongsakorn Sunthrayuth
Author:
Prasit Cholamjiak
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