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On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications

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Abstract

This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable suggestions, which helped us to present this paper in a better way.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Bing Tan & Songxiao Li

  2. Department of Mathematics, Zhejiang Normal University, Zhejiang, China

    Xiaolong Qin

Authors
  1. Bing Tan
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  2. Songxiao Li
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  3. Xiaolong Qin
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Correspondence to Songxiao Li.

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Communicated by Gabriel Haeser.

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Tan, B., Li, S. & Qin, X. On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications. Comp. Appl. Math. 40, 253 (2021). https://doi.org/10.1007/s40314-021-01642-z

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  • DOI: https://doi.org/10.1007/s40314-021-01642-z

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