Improved inertial extragradient methods for solving pseudo-monotone variational inequalities

Abstract

Thong et al. (A strong convergence theorem for Tseng's extragradient method for solving variational inequality problems. Optim Lett. 2020;14:1157–1175) introduced inertial Tseng's extragradient method to variational inequality problems for monotone and Lipschitz continuous mappings. In this work, we extend this method for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm provides the strong convergence without using the viscosity technique, as well as the monotonicity of the associated mapping. The advantage of the second algorithm is that it does not require the knowledge of the Lipschitz constants of the variational inequality mappings. Finally, some numerical experiments illustrating the performance of our algorithms are discussed.

Keywords:

• Inertial Tseng's extragradient method
• Mann-type method
• variational inequality problem
• pseudo-monotone mapping
• strong convergence

2010 Mathematics Subject Classifications:

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

Acknowledgments

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

Disclosure statement

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

Additional information

Funding

This work was partially supported by the National Foundation for Science and Technology Development [grant number 101.01-2019.320].