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Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces

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Abstract

In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.

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Acknowledgements

We acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study.

Funding

This research is funded by University of Information Technology-Vietnam National University HoChiMinh City under grant number D1-2023-08.

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Authors and Affiliations

  1. Department of Mathematics and Physics, University of Information Technology, Ho Chi Minh City, Vietnam

    Le Huynh My Van & Dang Le Thuy

  2. Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam

    Le Huynh My Van

  3. Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam

    Le Huynh My Van & Dang Le Thuy

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

    Tran Viet Anh

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  1. Le Huynh My Van
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  2. Dang Le Thuy
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Correspondence to Tran Viet Anh.

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Van, L.H.M., Thuy, D.L. & Anh, T.V. Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces. Acta Math Vietnam 48, 459–478 (2023). https://doi.org/10.1007/s40306-023-00508-2

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  • DOI: https://doi.org/10.1007/s40306-023-00508-2

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