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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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Bibliographic Details
Published in:Computational & applied mathematics 2021-07, Vol.40 (5), Article 168
Main Authors: Dong, Qiao-Li, He, Songnian, Liu, Lulu
Format: Article
Language:English
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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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01540-4