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A Tseng extragradient method for solving variational inequality problems in Banach spaces

Abstract

This paper presents an inertial Tseng extragradient method for approximating a solution of the variational inequality problem. The proposed method uses a single projection onto a half space which can be easily evaluated. The method considered in this paper does not require the knowledge of the Lipschitz constant as it uses variable stepsizes from step to step which are updated over each iteration by a simple calculation. We prove a strong convergence theorem of the sequence generated by this method to a solution of the variational inequality problem in the framework of a 2-uniformly convex Banach space which is also uniformly smooth. Furthermore, we report some numerical experiments to illustrate the performance of this method. Our result extends and unifies corresponding results in this direction in the literature.

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Acknowledgements

The first author acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF CoE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF and CoE-MaSS.

The authors would like to thank the editor and anonymous reviewers for their invaluable suggestions which have greatly improved the manuscript.

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Correspondence to O. K. Oyewole.

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Oyewole, O.K., Abass, H.A., Mebawondu, A.A. et al. A Tseng extragradient method for solving variational inequality problems in Banach spaces. Numer Algor (2021). https://doi.org/10.1007/s11075-021-01133-6

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Keywords

  • Variational inequality
  • Pseudomonotone operator
  • Strong convergence
  • Banach space
  • Extragradient algorithm
  • Step-size rule

Mathematics Subject Classification 2010

  • 47H09
  • 49J35
  • 90C47