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The Galerkin Method and Regularization for Variational Inequalities in Reflexive Banach Spaces

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Abstract

This paper studies the convergence of the Galerkin method and regularization for variational inequalities with pseudomonotone operators in the sense of Brézis. Namely, we prove that under certain conditions, the solutions of the Galerkin equations and regularized variational inequalities converge strongly to a solution of the original variational inequality in reflexive Banach spaces. An application for obstacle problems is given.

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Acknowledgements

The authors would like to thank the anonymous referees for their suggestions and comments which improved the paper greatly. The research of C.F. Wen was funded by Ministry of Science and Technology, Taiwan, under grant number 109-2115-M-037-001.

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Authors and Affiliations

  1. Faculty of Computer Science and Information Technology, Quang Trung University, 327 Dao Tan Street, Qui Nhon City, Binh Dinh province, Vietnam

    Bui Trong Kien

  2. Department of Mathematics, Yibin University, Yibin, China

    Xiaolong Qin

  3. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

  4. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

  5. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  6. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

    Jen-Chih Yao

Authors
  1. Bui Trong Kien
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  2. Xiaolong Qin
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  3. Ching-Feng Wen
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  4. Jen-Chih Yao
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Corresponding author

Correspondence to Ching-Feng Wen.

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Communicated by Akhtar A. Khan.

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Kien, B.T., Qin, X., Wen, CF. et al. The Galerkin Method and Regularization for Variational Inequalities in Reflexive Banach Spaces. J Optim Theory Appl 189, 578–596 (2021). https://doi.org/10.1007/s10957-021-01844-9

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  • DOI: https://doi.org/10.1007/s10957-021-01844-9

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