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Dynamical Systems for Solving Variational Inequalities

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Abstract

In this paper, we propose dynamical systems for solving variational inequalities whose mapping is paramonotone, strongly pseudomonotone or pseudomonotone and Lipschitz continuous, respectively. Solutions of these dynamical system are shown to converge to a desired solution of the variational inequalities. When the mapping is strongly pseudomonotone but is not necessarily Lipschitz continuous, the convergence rate of the new algorithm is established. This approach is novel and the new algorithms can be considered continuous versions of the existing ones for variational inequalities.

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Acknowledgements

The author would like to thank the anonymous referees for their remarks which helped to significantly improve the paper.

Funding

This work is supported by Vietnam Ministry of Education and Training under grant number B2020-BKA-21-CTTH.

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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

    Trinh Ngoc Hai

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  1. Trinh Ngoc Hai
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Correspondence to Trinh Ngoc Hai.

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Hai, T.N. Dynamical Systems for Solving Variational Inequalities. J Dyn Control Syst 28, 681–696 (2022). https://doi.org/10.1007/s10883-021-09531-8

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  • DOI: https://doi.org/10.1007/s10883-021-09531-8

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