Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities
Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities
In this paper, we introduce and analyze two new inertial-like algorithms with the Bregman divergences for solving the pseudomonotone variational inequality problem in a real Hilbert space. The first algorithm is inspired by the Halpern-type iteration and the subgradient extragradient method and the second algorithm is inspired by the Halpern-type iteration and Tseng’s extragradient method. Under suitable conditions, we prove some strong convergence theorems of the proposed algorithms without assuming the Lipschitz continuity and the sequential weak continuity of the given mapping. Finally, we give some numerical experiments with various types of Bregman divergence to illustrate the main results. In fact, the results presented in this paper improve and generalize the related works in the literature.
Bregman divergence, Hilbert space, Pseudomonotone mapping, Strong convergence, Variational inequality problem
Jolaoso, Lateef Olakunle
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Sunthrayuth, Pongsakorn
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Cholamjiak, Prasit
ca478763-4dff-4e84-b521-ec266b1cfc47
Cho, Yeol Je
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1 October 2022
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
(2022)
Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities.
Computational and Applied Mathematics, 41 (7), [300].
(doi:10.1007/s40314-022-02006-x).
Abstract
In this paper, we introduce and analyze two new inertial-like algorithms with the Bregman divergences for solving the pseudomonotone variational inequality problem in a real Hilbert space. The first algorithm is inspired by the Halpern-type iteration and the subgradient extragradient method and the second algorithm is inspired by the Halpern-type iteration and Tseng’s extragradient method. Under suitable conditions, we prove some strong convergence theorems of the proposed algorithms without assuming the Lipschitz continuity and the sequential weak continuity of the given mapping. Finally, we give some numerical experiments with various types of Bregman divergence to illustrate the main results. In fact, the results presented in this paper improve and generalize the related works in the literature.
Text
Analysis of two versions of relaxed inertial algorithms
- Accepted Manuscript
More information
Accepted/In Press date: 25 June 2022
e-pub ahead of print date: 3 September 2022
Published date: 1 October 2022
Additional Information:
Funding Information:
The authors would like to thank Associate Editor and anonymous referee for valuable comments. P. Sunthrayuth was supported by Rajamangala University of Technology Thanyaburi (RMUTT). P. Cholamjiak was supported by the Thailand Science Research and Innovation Fund, and University of Phayao (Grant no. FF65-UoE001) and School of Science, University of Phayao (Grant no. PBTSC65013).
Publisher Copyright:
© 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
Keywords:
Bregman divergence, Hilbert space, Pseudomonotone mapping, Strong convergence, Variational inequality problem
Identifiers
Local EPrints ID: 470916
URI: http://eprints.soton.ac.uk/id/eprint/470916
ISSN: 2238-3603
PURE UUID: aedb83ee-2ab0-46a4-97eb-5dcc82373fdc
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Date deposited: 21 Oct 2022 16:30
Last modified: 17 Mar 2024 07:33
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Contributors
Author:
Pongsakorn Sunthrayuth
Author:
Prasit Cholamjiak
Author:
Yeol Je Cho
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