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Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators

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Abstract

In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.

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Acknowledgements

The authors would like to thank the Editor and the anonymous referee for their valuable comments, which greatly improved the quality of the initial manuscript.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Bing Tan

  2. Department of Mathematics, Zhejiang Normal University, Zhejiang, China

    Xiaolong Qin

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  1. Bing Tan
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  2. Xiaolong Qin
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Correspondence to Xiaolong Qin.

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Tan, B., Qin, X. Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators. Anal.Math.Phys. 12, 26 (2022). https://doi.org/10.1007/s13324-021-00638-6

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