Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems

Abstract

The subgradient extragradient method can be considered as an improvement of the extragradient method for variational inequality problems for the class of monotone and Lipschitz continuous mappings. In this paper, we propose two new algorithms as combination between the subgradient extragradient method and Mann-like method for finding a common element of the solution set of a variational inequality and the fixed point set of a demicontractive mapping.

Keywords:

• Subgradient extragradient method
• extragradient method
• Mann-like method
• variational inequality problem
• fixed point problem
• demicontractive mapping

Acknowledgements

The authors would like to thank the two referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author was partially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2017.315].