Three novel inertial explicit Tseng's extragradient methods for solving pseudomonotone variational inequalities

Abstract

In this paper, we construct three new extragradient-type iterative methods for solving variational inequalities in real Hilbert spaces. The proposed iterative methods are functionally equivalent to the extragradient method, which is used to solve variational inequalities in an infinite-dimensional real Hilbert space. The main advantage of these iterative methods is that they use a simple step size rule based on operator information instead of the Lipschitz constant or any line search method. Three strong convergence theorems are well proved, corresponding to the proposed methods by allowing certain control parameter conditions. Finally, we present some numerical experiments to verify the efficacy and superiority of the proposed iterative methods.

Keywords:

• Variational inequalities
• Tseng's extragradient method
• inertial methods
• pseudomonotone mapping
• strong convergence theorem

2010 Mathematics Subject Classifications:

• 65Y05
• 65K15
• 68W10
• 47H05
• 47H10

Acknowledgments

We would like to thank the associate editor and referees for their comments and suggestions on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.