New subgradient extragradient algorithm for solving variational inequalities in Hadamard manifold

Abstract

This paper introduces a schematic approximation method for a solution to a variational inequality problem in the framework of Hadamard manifold. The method is a combination of the subgradient extragradient technique and Popov extragradient method. Using this method, some convergence algorithms were proved when the cost operators are pseudomonotone and strongly pseudomonotone, respectively. In the construction of this method, the dependence on Lipschitz constants of the operators is dispensed with by the use of a monotone decreasing step size. We give an application of our main result to the constrained convex minimization problem. Finally, we report some numerical examples to illustrate the efficiency and applicability of the method.

Keywords:

• Variational inequalities
• pseudomonotone
• extragradient method
• Hadamard manifold

Mathematics Subject Classifications:

• 47H09
• 49J25
• 65K10
• 90C25

Acknowledgments

The author is grateful to Dr. Feeroz Babu for his fruitful discussions on some of the results in the preliminaries. We are grateful to the anonymous reviewers whose comments have helped improved the quality of presentation of the manuscript.

Disclosure statement

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