Self-adaptive inertial extragradient algorithms for solving variational inequality problems

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the sugges...

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Bibliographic Details
Published in:Computational & applied mathematics 2021-02, Vol.40 (1), Article 19
Main Authors: Tan, Bing, Fan, Jingjing, Li, Songxiao
Format: Article
Language:English
Subjects:
Adaptive algorithms
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Convergence
Hilbert space
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01393-3