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Accelerated Subgradient Extragradient Methods for Variational Inequality Problems

  • Duong Viet ThongEmail author
  • Nguyen The Vinh
  • Yeol Je Cho
Article

Abstract

In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based on the inertial subgradient extragradient algorithm, the viscosity approximation method and the Mann type method, and prove some strong convergence theorems for the proposed algorithms under suitable conditions. The main results in this paper improve and extend some recent works given by some authors. Finally, the performances and comparisons with some existing methods are presented through several preliminary numerical experiments.

Keywords

Variational inequality problem Extragradient method Subgradient extragradient method Inertial method Mann type method Viscosity method 

Mathematics Subject Classification

65Y05 65K15 68W10 47H05 47H10 

Notes

Acknowledgements

The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.08.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of MathematicsUniversity of Transport and CommunicationsHanoi CityVietnam
  3. 3.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  4. 4.Department of Mathematics Education and the RINSGyeongsang National UniversityJinjuKorea

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