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An improved relaxed inertial projection algorithm for solving the minimum-norm solution of variational inequality and fixed point problems

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Abstract

In this paper, a modified projection algorithm is proposed in order to solve a common element of the solution set of monotone variational inequality and the fixed point set of a class of quasi-pseudo-contractive mapping. This algorithm requires the monotonicity and Lipschitz continuity of the mapping, but don’t need to know Lipschitz constant. On one hand, this algorithm does not compute the projection onto the feasible set at each iteration, on the other hand, the strong convergence of the sequence generated by the algorithm can be obtained without viscosity technology, and the convergence rate of the algorithm better than some algorithms, and the effect of the algorithm is illustrated by two numerical experiments.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Funding

This research was funded by National Natural Science Foundation of China (Grant No. 11872043), Natural Science Foundation of Sichuan Province (Grant No. 2023NSFSC1299), Fund Project of Sichuan University of Science and Engineering in hit-haunting for talents (Grant No. 2022RC04), 2021 Innovation and Entrepreneurship Training Program for College Students of Sichuan University of Science and Engineering (Grant No. cx2021150), 2022 Graduate Innovation Project of Sichuan University of Science and Engineering (Grant No. Y2022190).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, Sichuan, China

    Huan Zhang, Xiaolan Liu, Jia Deng & Yan Sun

  2. South Sichuan Center for Applied Mathematics, Zigong, 643000, Sichuan, China

    Xiaolan Liu

  3. Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, 643000, Sichuan, China

    Xiaolan Liu

Authors
  1. Huan Zhang
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  2. Xiaolan Liu
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  3. Jia Deng
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  4. Yan Sun
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Contributions

Conceptualisation of the article and methodology were given by HZ; formal analysis, investigation, and writing-original draft preparation by HZ and JD; software and validation by HZ and XLL, writing-review and editing by HZ, YS, and JD. All authors read and approved the final manuscript.

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Correspondence to Xiaolan Liu.

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Zhang, H., Liu, X., Deng, J. et al. An improved relaxed inertial projection algorithm for solving the minimum-norm solution of variational inequality and fixed point problems. J. Appl. Math. Comput. 69, 2717–2739 (2023). https://doi.org/10.1007/s12190-023-01853-z

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  • DOI: https://doi.org/10.1007/s12190-023-01853-z

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