A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems

Abstract

This paper develops a two-step extragradient-viscosity method for finding a common solution to a variational inequality problem and a fixed point problem in a Hilbert space. Combining the two-step extragradient algorithm and the viscosity one, we propose a strongly convergent method, which contains as special cases some existing algorithms. Several numerical experiments are implemented to demonstrate the performance of the proposed method in comparison with classical hybrid extragradient-like algorithms.

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Acknowledgements

The authors would like to thank the Associate Editor and anonymous referees for their valuable comments and suggestions which help us in improving the original version of this paper.

Funding

The first-named and last-named authors are supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project: 101.01-2017.315.

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Correspondence to Dang Van Hieu.

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Van Hieu, D., Son, D.X., Anh, P.K. et al. A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems. Acta Math Vietnam 44, 531–552 (2019). https://doi.org/10.1007/s40306-018-0290-z

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Keywords

  • Variational inequality
  • Fixed point problem
  • Monotone operator
  • Demicontractive mapping
  • Extragradient method
  • Viscosity method
  • Hybrid method

Mathematics Subject Classification (2010)

  • 65J15
  • 47H05
  • 47J25
  • 47J20
  • 91B50