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The projection and contraction methods for finding common solutions to variational inequality problems

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Abstract

In this paper, we firstly introduce two projection and contraction methods for finding common solutions to variational inequality problems involving monotone and Lipschitz continuous operators in Hilbert spaces. Then, by modifying the two methods, we propose two hybrid projection and contraction methods. Both weak and strong convergence are investigated under standard assumptions imposed on the operators. Also, we generalize some methods to show the existence of solutions for a system of generalized equilibrium problems. Finally, some preliminary experiments are presented to illustrate the advantage of the proposed methods.

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Acknowledgements

We would like to express their thanks to Dr. Hieu for his help in program. We wish to thank the anonymous referees for the careful readings and suggestions, which led to improvements in the presentation of the results.

Supported by National Natural Science Foundation of China (No. 71602144) and Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2016ASP-TJ01)

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Authors and Affiliations

  1. Tianjin Key Lab for Advanced Signal Processing, College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

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

    Yeol Je Cho

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

    Yeol Je Cho

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

    Themistocles M. Rassias

Authors
  1. Qiao-Li Dong
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  2. Yeol Je Cho
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  3. Themistocles M. Rassias
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Correspondence to Qiao-Li Dong or Yeol Je Cho.

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Dong, QL., Cho, Y.J. & Rassias, T.M. The projection and contraction methods for finding common solutions to variational inequality problems. Optim Lett 12, 1871–1896 (2018). https://doi.org/10.1007/s11590-017-1210-1

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