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A general inertial projected gradient method for variational inequality problems
The purpose of this article is to introduce a general inertial projected gradient method with a self-adaptive stepsize for solving variational inequality problems. The proposed method incorporates two different extrapolations with respect to the previous iterates into the projected gradient method....
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Published in: | Computational & applied mathematics 2021-07, Vol.40 (5), Article 168 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | The purpose of this article is to introduce a general inertial projected gradient method with a self-adaptive stepsize for solving variational inequality problems. The proposed method incorporates two different extrapolations with respect to the previous iterates into the projected gradient method. The weak convergence for our method is proved under standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping. Furthermore, R-linear convergence rate is established under the strong monotonicity assumption of the mapping. Finally preliminary results from numerical experiments and applications to optimal control problems are performed which show the advantage of the proposed method. |
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ISSN: | 2238-3603 1807-0302 |
DOI: | 10.1007/s40314-021-01540-4 |