The extragradient algorithm with inertial effects for solving the variational inequality

Abstract

In this article, we introduce an algorithms by incorporating inertial terms in the extragradient algorithm. A weak convergence theorem is established for the proposed algorithm. Numerical experiments show that the inertial algorithms speed up the original ones.

Keywords:

• Variational inequality
• extragradient algorithm
• inertial type algorithm
• weak convergence

Acknowledgements

The authors would like to thank two anonymous referees for their very thorough comments and constructive suggestions which enabled us to improve the paper greatly. In particular, we made significant modifications to Lemma 3.1 and Example 4.1 according to referees’ opinion.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61379102]; Fundamental Research Funds for the Central Universities [grant number 3122016L006], in part by the Foundation of Tianjin Key Lab for Advanced Signal Processing.