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A Strongly Convergent Subgradient Extragradient-Halpern Method for Solving a Class of Bilevel Pseudomonotone Variational Inequalities

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Abstract

We propose an algorithm which can be considered as a combination between the subgradient and Halpern methods for strongly monotone bilevel variational inequalities where the lower problem is a pseudomonotone variational inequality. The strong convergence of the sequences generated by the algorithm is proved.

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Acknowledgments

The author is very grateful to the two anonymous referees, the editor, and Professor Le Dung Muu for their useful comments and advices that helped the author very much in revising the paper.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Tran Viet Anh

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  1. Tran Viet Anh
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Correspondence to Tran Viet Anh.

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Anh, T.V. A Strongly Convergent Subgradient Extragradient-Halpern Method for Solving a Class of Bilevel Pseudomonotone Variational Inequalities. Vietnam J. Math. 45, 317–332 (2017). https://doi.org/10.1007/s10013-016-0196-9

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  • DOI: https://doi.org/10.1007/s10013-016-0196-9

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