Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems

  • Duong Viet ThongEmail author
  • Dang Van Hieu
  • Themistocles M. Rassias
Original Paper


In this paper, two new algorithms are introduced for solving a pseudomontone variational inequality problem with a Lipschitz condition in a Hilbert space. The algorithms are constructed around three methods: the subgradient extragradient method, the inertial method and the viscosity method. With a new stepsize rule is incorporated, the algorithms work without any information of Lipschitz constant of operator. The weak convergence of the first algorithm is established, while the second one is strongly convergent which comes from the viscosity method. In order to show the computational effectiveness of our algorithms, some numerical results are provided.


Subgradient extragradient method Inertial method Variational inequality Pseudomonotone mapping Lipschitz continuity 



The authors would like to thank anonymous reviewrs for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This work is supported by Vietnam (National Foundation for Science and Technology Development (NAFOSTED)) under the project: 101.01-2019.320.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Duong Viet Thong
    • 1
    Email author
  • Dang Van Hieu
    • 2
  • Themistocles M. Rassias
    • 3
  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of MathematicsCollege of Air ForceNha TrangVietnam
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece

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