Numerical Algorithms

, Volume 80, Issue 3, pp 741–752 | Cite as

Strong convergence result for solving monotone variational inequalities in Hilbert space

  • Jun Yang
  • Hongwei LiuEmail author
Original Paper


In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real Hilbert space. The algorithm is inspired by Tseng’s extragradient method and the viscosity method with a simple step size. A strong convergence theorem for our algorithm is proved without any requirement of additional projections and the knowledge of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to show the efficiency and advantage of the proposed algorithm.


Variational inequalities Projection Extragradient method Monotone mapping Convex set 

Mathematics Subject Classification (2010)

47J20 90C25 90C30 90C52 


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The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped to improve the original version of this paper.

Funding information

The Project was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2017JM1014).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematics and Information ScienceXianyang Normal UniversityXianyangChina

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