Iterative approximation of common solution to variational inequality problems in Hadamard manifold

Abstract

The aim of this paper is to introduce a forward-backward-forward algorithm with inertial extrapolation to solve the problem of finding a common solution to the variational inequality problem (CSVIP) in a Hadamard manifold. Using a self-adaptive step size, we obtain convergence results under some standard conditions. Numerical examples are given to illustrate the theoretical analysis. Our result is a generalization and extension of previously announced results in this direction in the literature.

KEYWORDS:

• Variational inequality
• forward-backward-forward algorithm
• inertial extrapolation
• Hadamard manifold

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 65K10
• 90C25

Acknowledgments

All the authors approved the final version of this manuscript. All the authors understand the purpose of the research and their individual roles. All the authors contributed equally to the final version of the manuscript.

Disclosure statement

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