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Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

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Abstract

This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.

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Acknowledgements

The authors are very grateful to the editors and reviewers for their valuable and constructive comments that greatly improved the readability and quality of the initial version of the manuscript. This paper was supported by the National Natural Science Foundation of China under Grant No. 11401152.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Bing Tan

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

    Xiaolong Qin

  3. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

    Jen-Chih Yao

  4. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Jen-Chih Yao

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  1. Bing Tan
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  2. Xiaolong Qin
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  3. Jen-Chih Yao
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Correspondence to Xiaolong Qin.

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Tan, B., Qin, X. & Yao, JC. Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems. J Glob Optim 82, 523–557 (2022). https://doi.org/10.1007/s10898-021-01095-y

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