Computational Optimization and Applications

, Volume 66, Issue 1, pp 75–96 | Cite as

Modified hybrid projection methods for finding common solutions to variational inequality problems

  • Dang Van Hieu
  • Pham Ky Anh
  • Le Dung MuuEmail author


In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators. Based on differently constructed half-spaces, the proposed methods reduce the number of projections onto feasible sets as well as the number of values of operators needed to be computed. Strong convergence theorems are established under standard assumptions imposed on the operators. An extension of the proposed algorithm to a system of generalized equilibrium problems is considered and numerical experiments are also presented.


Variational inequality Equilibrium problem Generalized equilibrium problem Gradient method Extragradient method 

Mathematics Subject Classification

65Y05 65K15 68W10 47H05 47H10 



The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The work of the second and third authors is supported by VIASM.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsVietnam National University, HanoiHanoiVietnam
  2. 2.Institute of MathematicsVAST, HanoiHanoiVietnam

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