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A new inertial double-projection method for solving variational inequalities

  • Aviv GibaliEmail author
  • Dang Van HieuEmail author
Article

Abstract

In this paper, we introduce a new algorithm of inertial form for solving monotone variational inequalities (VI) in real Hilbert spaces. Motivated by the subgradient extragradient method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity and Lipschitz continuity of the VI associated mapping, we establish the weak convergence of the scheme. Several numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature.

Keywords

Subgradient extragradient method inertial effect variational inequality monotone operator Lipschitz continuity 

Mathematics Subject Classification

Primary 65J15 47H05 Secondary 47J25 47J20 

Notes

Acknowledgements

The authors would like to thank the associate editor and two anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project 101.01-2017.315.

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Copyright information

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Authors and Affiliations

  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael
  2. 2.The Center for Mathematics and Scientific ComputationUniversity of HaifaHaifaIsrael
  3. 3.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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