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Strong convergence theorems by an extragradient-like approximation methods for quasi-variational inequalities

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Abstract

The goal of this paper is to study convergence of extragradient-like approximation methods for quasi-variational inequalities with the moving set. First, we propose the extragradient dynamical system and under strong monotonicity we show strong convergence with exponential rate of generated trajectory to the unique solution of quasi-variational inequality. Further, the explicit time discretization of this dynamical system leads to an extragradient algorithm with relaxation parameters. We prove the convergence of the generated iterative sequence to the unique solution of the quasi-variational inequality and derive the linear convergence rate under strong monotonicity.

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Acknowledgements

The authors are very grateful to the referees for their valuable comments on the paper.

Funding

This research was supported by the Montenegrin Academy of Sciences and Arts (project: Optimization with coupled constraints. Variational and quasi-variational inequalities).

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Authors and Affiliations

  1. Department of Mathematics, University of Montenegro, 2 Cetinjski put, Podgorica, 81000, Montenegro

    Nevena Mijajlović

  2. Montenegrin Academy of Sciences and Arts, 5 Rista Stijovica, Podgorica, 81000, Montenegro

    Milojica Jaćimović

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  1. Nevena Mijajlović
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  2. Milojica Jaćimović
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Correspondence to Nevena Mijajlović.

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Mijajlović, N., Jaćimović, M. Strong convergence theorems by an extragradient-like approximation methods for quasi-variational inequalities. Optim Lett 17, 901–916 (2023). https://doi.org/10.1007/s11590-022-01871-z

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