Self-adaptive inertial subgradient extragradient algorithm for solving pseudomonotone variational inequalities

ABSTRACT

In this paper, we introduce an inertial algorithm for solving classical variational inequalities with Lipschitz continuous and pseudomonotone mapping in real Hilbert space. The algorithm is inspired by subgradient extragradient method and the inertial method with a new step size. The convergence of algorithm is established without the knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are presented to show the efficiency and advantage of the proposed algorithm.

KEYWORDS:

• Variational inequalities
• projection
• subgradient extragradient method
• pseudomonotone mapping
• convex set

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47J20
• 90C25
• 90C30
• 90C52

Acknowledgments

The author would like to thank the Editor and the anonymous referees for their valuable comments and suggestions which helped to improve the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.