Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities

  • Duong Viet ThongEmail author
  • Aviv Gibali


The purpose of this paper is to study and analyze two new extragradient methods for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems of the proposed methods are established. We present academic and numerical examples for illustrating the behavior of the proposed algorithms.


Extragradient method Halpern method variational inequality pseudo-monotone operator 

Mathematics Subject Classification

65J15 65Y05 47H05 47J25 



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


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Copyright information

© 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.Department of MathematicsORT Braude CollegeKarmielIsrael
  3. 3.The Center for Mathematics and Scientific ComputationUniversity of HaifaHaifaIsrael

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