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Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators

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Abstract

In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results obtained in this paper extend and improve some related works in the literature.

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Acknowledgements

The authors sincerely thank the Editor and the anonymous reviewers for their careful reading and suggestions that improved the manuscript. This work was supported by the NSF of China (Grant No. 11771063), the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0455), Science and Technology Project of Chongqing Education Committee (Grant No. KJZD-K201900504), the University Young Core Teacher Foundation of Chongqing (020603011714).

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Authors and Affiliations

  1. School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Gang Cai

  2. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong & Yu Peng

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  1. Gang Cai
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  2. Qiao-Li Dong
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  3. Yu Peng
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Correspondence to Gang Cai.

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Communicated by Jen-Chih Yao.

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Cai, G., Dong, QL. & Peng, Y. Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators. J Optim Theory Appl 188, 447–472 (2021). https://doi.org/10.1007/s10957-020-01792-w

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