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An alternated inertial method for pseudomonotone variational inequalities in Hilbert spaces

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Abstract

In this paper, we introduce a new relaxed extrgadient algorithm with alternated inertial extrapolation step and self adaptive variable stepsizes for solving variational inequality problems whose cost operator is pseudomonotone operator in Hilbert spaces. We establish the weak convergence of the proposed algorithm and linear convergence under some standard assumptions. Numerical experiments are given to support theoretical results and comparison with recent related methods.

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Acknowledgements

The authors wish to thank the two anonymous referees for their excellent comments and suggestions which have helped to improve the presentation of the latest version of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Ferdinard U. Ogbuisi

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

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

    Jen-Chih Yao

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

    Jen-Chih Yao

Authors
  1. Ferdinard U. Ogbuisi
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  2. Yekini Shehu
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  3. Jen-Chih Yao
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Correspondence to Ferdinard U. Ogbuisi.

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Ogbuisi, F.U., Shehu, Y. & Yao, JC. An alternated inertial method for pseudomonotone variational inequalities in Hilbert spaces. Optim Eng 23, 917–945 (2022). https://doi.org/10.1007/s11081-021-09615-1

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  • DOI: https://doi.org/10.1007/s11081-021-09615-1

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