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Acta Mathematica Vietnamica

, Volume 42, Issue 4, pp 761–773 | Cite as

Convergence Theorems for Variational Inequalities on the Solution Set of Ky Fan Inequalities

  • Pham Ngoc AnhEmail author
  • Tran T. H. Anh
  • Takahito Kuno
Article

Abstract

Based on the subgradient methods and fixed point techniques, we develop a new iteration method for solving variational inequalities on the solution set of Ky Fan inequalities. The convergence for the proposed algorithms to the solution is guaranteed under certain assumptions in the Euclidean space \(\mathcal R^{n}\).

Keywords

Variational inequalities Ky Fan inequalities Strongly monotone Lipschitz continuous Global convergence 

Mathematics Subject Classification (2010)

65 K10 90 C25 

Notes

Acknowledgements

We are very grateful to anonymous referees for their helpful and constructive comments that helped us very much in improving the paper.

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number “101.02-2017.15.”

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Pham Ngoc Anh
    • 1
    Email author
  • Tran T. H. Anh
    • 2
  • Takahito Kuno
    • 3
  1. 1.Laboratory of Applied Mathematics and ComputingPTITHanoiVietnam
  2. 2.Department of MathematicsHaiphong UniversityHaiphongVietnam
  3. 3.Department of Computer ScienceUniversity of TsukubaIbarakiJapan

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