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A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems

  • Prasit Cholamjiak
  • Duong Viet ThongEmail author
  • Yeol Je Cho
Article
  • 49 Downloads

Abstract

In this paper, we introduce a new algorithm which combines the inertial contraction projection method and the Mann-type method (Mann in Proc. Am. Math. Soc. 4:506–510, 1953) for solving monotone variational inequality problems in real Hilbert spaces. The strong convergence of our proposed algorithm is proved under some standard assumptions imposed on cost operators. Finally, we give some numerical experiments to illustrate the proposed algorithm and the main result.

Keywords

Inertial contraction projection method Mann-type method Pseudomonotone mapping Pseudomonotone variational inequality problem 

Mathematics Subject Classification (2010)

65Y05 65K15 68W10 47H05 47H10 

Notes

Acknowledgements

The authors would like to thank three anonymous reviewers 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. P. Cholamjiak was supported by Thailand Research Fund and University of Phayao under the project RSA6180084 and UOE62001. This work was partially supported by Thailand Science Research and Innovation under the project IRN62W0007.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Prasit Cholamjiak
    • 1
  • Duong Viet Thong
    • 2
    Email author
  • Yeol Je Cho
    • 3
    • 4
  1. 1.School of ScienceUniversity of PhayaoPhayaoThailand
  2. 2.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Department of Mathematics EducationGyeongsang National UniversityJinjuKorea
  4. 4.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduP.R. China

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