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Regularization Proximal Method for Monotone Variational Inclusions

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Abstract

The paper concerns with a new iterative method for solving a monotone variational inclusion problem in a Hilbert space. The method is of the proximal contraction type incorporated with the regularization technique. Under the prediction stepsize conditions, we establish the strong convergence of the iterative sequences generated by the method to a particular solution of the problem satisfying a variational inequality problem. Finally, we give some numerical examples to illustrate the behavior of the new method in comparison with existing ones.

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Acknowledgements

The authors sincerely thank the Editor and two anonymous referees for their valuable comments and suggestions which helped us to improve the original version of this paper. The research of the first author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.06.

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Authors and Affiliations

  1. TIMAS - Thang Long University, Hanoi, Vietnam

    Dang Van Hieu

  2. Department of Mathematics, Vietnam National University, Hanoi, Vietnam

    Pham Ky Anh

  3. Faculty of Basic Sciences, University of Transport and Communications, Hanoi, Vietnam

    Nguyen Hai Ha

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  1. Dang Van Hieu
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  2. Pham Ky Anh
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  3. Nguyen Hai Ha
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Correspondence to Dang Van Hieu.

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Van Hieu, D., Anh, P.K. & Ha, N.H. Regularization Proximal Method for Monotone Variational Inclusions. Netw Spat Econ 21, 905–932 (2021). https://doi.org/10.1007/s11067-021-09552-7

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