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A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions

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Abstract

In this paper, we introduce a new class of hybrid inertial and contraction proximal point algorithm for the variational inclusion problem of the sum of two mappings in Hilbert spaces. We prove that the proposed algorithm converges strongly to a solution of the variational inclusion problem whenever its solution set is nonempty and the single-valued mapping f is Lipschitz continuous, monotone, and the set-valued mapping \({\mathscr{A}}\) is maximal monotone in infinite-dimensional real Hilbert spaces. Our work generalize and extend some related existing results in the literature. Finally, we illustrate the numerical performance of our Algorithm 1 and we give an application to the split feasibility problem.

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The author acknowledges that the data presented in this study must be deposited and made publicly available in an acceptable repository, prior to publication.

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Acknowledgements

The author would like to thank the referee for his valuable suggestions to improve the earlier version of this paper.

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  1. Department of Mathematics, The Technion- Israel Institute of Technology, Haifa, 3200003, Israel

    Soumitra Dey

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Dey, S. A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions. Numer Algor 93, 1–25 (2023). https://doi.org/10.1007/s11075-022-01400-0

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