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Dynamical System Modeling and Stability Investigation�DSMSI-2023

Dedicated to the 77th anniversary of the outstanding Ukrainian scientist

professor Denys Khusainov

December 19-21, 2023, Kyiv, Ukraine

The Regularized Operator Extrapolation Algorithm

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Vladimir Semenov, semenov.volodya@gmail.com

Oleh Kharkov, olehharek@gmail.com

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Taras Shevchenko National University of Kyiv

Faculty of Computer Science and Cybernetics

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Preliminaries and problem statement�

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Preliminaries and problem statement�

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Preliminaries and problem statement�

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Modificated methods�

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Regularized Operator Algorithm�

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Strong convergence. Basic lemmas

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Strong convergence. Basic lemmas

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Strong convergence. Auxiliary lemmas

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Strong convergence. Auxiliary lemmas

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Strong convergence. Main result

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Further research�

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Conclusions�

  • In this talk a new iterative algorithm for solving variational inequalities in Hilbert spaces was proposed and investigated.

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  • This algorithm is a regularized (by applying the Halpern scheme) variant of the Operator Extrapolation Method.

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  • For variational inequalities with monotone Lipschitz continuous operators, acting in Hilbert space, the strong convergence theorem of this method was proved.

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Dynamical System Modeling and Stability Investigation, DSMSI-2023

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Thank you for your attention