Variational inequalities governed by strongly pseudomonotone vector fields on Hadamard manifolds

Abstract

We consider variational inequalities governed by strongly pseudomonotone vector fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a modified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate our results.

Keywords:

• Variational inequalities
• Hadamard manifolds
• strongly pseudomonotone
• modified projection method
• linear conditioning
• Finite convergence

2020 Mathematics Subject Classifications:

• 49J40
• 58D17
• 90C33

Acknowledgements

We are grateful to the anonymous referees for their valuable suggestions and remarks that allowed us to improve the original presentation of the paper.

Disclosure statement

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

Additional information

Funding

Nguyen Thai An acknowledges the support of Hue University under the Core Research Program [grant number NCM.DHH.2020.02].