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Inertial projection and contraction algorithms for variational inequalities

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Abstract

In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.

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Acknowledgements

The authors express their thanks to the reviewers, whose constructive suggestions led to improvements in the presentation of the results.

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Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Q. L. Dong

  2. Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China, Tianjin, 300300, China

    Q. L. Dong & L. L. Zhong

  3. Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, 660-701, Korea

    Y. J. Cho

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Y. J. Cho

  5. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Th. M. Rassias

Authors
  1. Q. L. Dong
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  2. Y. J. Cho
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  3. L. L. Zhong
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  4. Th. M. Rassias
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Corresponding author

Correspondence to Y. J. Cho.

Additional information

The first author was supported by National Natural Science Foundation of China (No. 61379102) and Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2016ASP-TJ01), the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2014R1A2A2A01002100) and the third author was supported by Tianjin Research Program of Application Foundation and Advanced Technology (No. 15JCQNJC04400).

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Dong, Q.L., Cho, Y.J., Zhong, L.L. et al. Inertial projection and contraction algorithms for variational inequalities. J Glob Optim 70, 687–704 (2018). https://doi.org/10.1007/s10898-017-0506-0

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  • DOI: https://doi.org/10.1007/s10898-017-0506-0

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