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Acta Mathematica Vietnamica

, Volume 44, Issue 3, pp 639–663 | Cite as

Inertial Extragradient Algorithms for Solving Equilibrium Problems

  • Nguyen The Vinh
  • Le Dung MuuEmail author
Article
  • 29 Downloads

Abstract

We introduce two new algorithms based upon the extragradient and inertial methods for solving pseudomonotone equilibrium problems in real Hilbert spaces. Strong converge and weak convergence of the proposed algorithms are established under some mild assumptions. Numerical results show that the proposed algorithms are more efficient than some existing methods for equilibrium problems.

Keywords

Inertial method Extragradient algorithm Variational inequality Equilibrium problem Pseudomonotone Lipschitz-type inequality 

Mathematics Subject Classification (2010)

47H10 47J25 47N10 90C25 

Notes

Acknowledgments

The authors would like to thank the editor and referee for careful reading, and constructive suggestions that allowed to improve significantly the presentation of this paper.

Funding Information

The first 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

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Transport and CommunicationsHanoiVietnam
  2. 2.TIMASThang Long UniversityHanoiVietnam
  3. 3.Institute of Mathematics, VASTHanoiVietnam

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