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A modified inertial Tseng technique of Bilevel variational inequality problem with application to image processing

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Abstract

In this paper, we propose and study a new modified Tseng inertial iterative technique for solving Bilevel quasimonotone Variational Inequality Problem (BVIP) in the framework of Hilbert spaces. In addition, we establish a strong convergence result of the proposed iterative technique under some mild assumptions, the proposed iterative technique does not need prior knowledge of Lipschitz’s constant of the quasimonotone operator. Finally, we present a numerical example of our proposed methods in comparison with some recent results in the literature, also, we apply our iterative technique to image deblurring and optimal control problems.

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Acknowledgements

The authors wish to thank the anonymous reviewers for their useful comments that greatly improve the paper.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria

    A. A. Mebawondu

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    A. A. Mebawondu, O. K. Narain, A. A. Onifade & F. A. Kasali

  3. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

    R. George

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Mebawondu, A.A., George, R., Narain, O.K. et al. A modified inertial Tseng technique of Bilevel variational inequality problem with application to image processing. J Anal (2024). https://doi.org/10.1007/s41478-024-00756-x

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