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

Acta Mathematica Vietnamica volume 42, pages761–773(2017)Cite this 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 \(\mathcal R^{n}\).

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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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Affiliations

  1. Laboratory of Applied Mathematics and Computing, PTIT, Hanoi, Vietnam

    Pham Ngoc Anh

  2. Department of Mathematics, Haiphong University, Haiphong, Vietnam

    Tran T. H. Anh

  3. Department of Computer Science, University of Tsukuba, Ibaraki, 305-8573, Japan

    Takahito Kuno

Authors
  1. Pham Ngoc Anh
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  2. Tran T. H. Anh
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  3. Takahito Kuno
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Correspondence to Pham Ngoc Anh.

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Anh, P.N., Anh, T.T.H. & Kuno, T. Convergence Theorems for Variational Inequalities on the Solution Set of Ky Fan Inequalities. Acta Math Vietnam 42, 761–773 (2017). https://doi.org/10.1007/s40306-017-0226-z

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Keywords

  • Variational inequalities
  • Ky Fan inequalities
  • Strongly monotone
  • Lipschitz continuous
  • Global convergence

Mathematics Subject Classification (2010)

  • 65 K10
  • 90 C25