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Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

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Abstract

The purpose of this paper is to investigate pseudomonotone variational inequalities in real Hilbert spaces. For solving this problem, we introduce a new method. The proposed algorithm combines the advantages of the subgradient extragradient method and the projection and contraction method. We establish the strong convergence of the proposed algorithm under conditions pseudomonotonicity and Lipschitz continuity assumptions. Moreover, under additional strong pseudomonotonicity and Lipschitz continuity assumptions, the linear convergence of the sequence generated by the proposed algorithm is obtained. Numerical examples provide to illustrate the potential of our algorithms as well as compare their performances to several related results.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are thankful to the handling editor and two anonymous reviewers for comments and remarks which substantially improved the quality of the paper. The authors would like to thank Professor Pham Ky Anh for drawing our attention to the subject and for many useful discussions. This research is funded by National Economics University, Hanoi, Vietnam.

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Correspondence to Vu Tien Dung.

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Thong, D.V., Li, X., Dong, QL. et al. Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces. Numer Algor 92, 2243–2274 (2023). https://doi.org/10.1007/s11075-022-01386-9

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