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Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces

  • Duong Viet ThongEmail author
  • Aviv Gibali
Original Paper Area 2
  • 90 Downloads

Abstract

In this paper we are focused on solving monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Motivated by several recent results related to the subgradient extragradient method (SEM), we propose two SEM extensions which do not require the knowledge of the Lipschitz constant associated with the variational inequality operator. Under mild and standard conditions, we establish the strong convergence of our schemes. Primary numerical examples demonstrate the potential of our algorithms as well as compare their performances to several related results.

Keywords

Projection and contraction method Subgradient extragradient method Mann type method Viscosity method Variational inequality problem 

Mathematics Subject Classification

47H09 47H10 47J20 47J25 

Notes

Acknowledgements

The authors would like to thank the referees for their comments on the manuscript which helped in improving earlier version of this paper.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of MathematicsORT Braude CollegeKarmielIsrael
  3. 3.The Center for Mathematics and Scientific ComputationUniversity of HaifaHaifaIsrael

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