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Results in Mathematics

, 74:137 | Cite as

Explicit Extragradient-Like Method with Regularization for Variational Inequalities

  • Dang Van HieuEmail author
  • Le Dung Muu
  • Pham Kim Quy
  • Le Van Vy
Article
  • 138 Downloads

Abstract

In this paper, we introduce and analyze the convergence of a new algorithm for solving a monotone and Lipschitz variational inequality problem in a Hilbert space. The algorithm uses variable stepsizes which are generated over each iteration, based on some previous iterates, and by some cheap computations. Contrary to many known algorithms, the resulting algorithm can be easily implemented without the prior knowledge of Lipschitz contant of operator, and also without any linesearch procedure. Besides, the regularization technique is suitably incorporated in the algorithm to get further convergence. Theorem of strong convergence is established under mild conditions imposed on control parameters. Some experiments are provided to illustrate the numerical behavior of the algorithm in comparison with others.

Keywords

Variational inequality monotone operator extragradient method subgradient extragradient method projection method 

Mathematics Subject Classification

65Y05 65K15 68W10 47H05 47H10 

Notes

Acknowledgements

The authors would like to thank the Editor and the referees for their comments on the manuscript which helped in improving earlier version of this paper. The first and second authors are supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.315.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.TIMASThang Long UniversityHa NoiVietnam
  3. 3.Department of MathematicsCollege of Air ForceNha Trang CityVietnam

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