Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds

ABSTRACT

This paper is devoted to two efficient algorithms for solving variational inequality on Hadamard manifolds. The algorithms are inspired by Tseng's extragradient methods with new step sizes, established without the knowledge of the Lipschitz constant of the mapping. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the methods converges to a solution of variational inequality, whenever it exists.

KEYWORDS:

• Variational inequalities
• extragradient method
• Hadamard manifolds
• pseudomonotone vector field

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47J20
• 51H25
• 65C10
• 65C15
• 90C33

Acknowledgments

The authors are grateful to the Co-Editor and referees for their valuable suggestions and corrections which helped to improve the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Xiaokai Chang was supported by the Hongliu Foundation of First-class Disciplines of Lanzhou University of Technology. The project was supported by the National Natural Science Foundation of China [grant number 61877046].