Double inertial projection method for variational inequalities with quasi-monotonicity

ABSTRACT

This paper presents a projection and contraction method with a double inertial extrapolation step and self-adaptive step sizes to solve variational inequalities with quasi-monotonicity in real Hilbert spaces. Weak and strong convergence results are obtained under some mild conditions. We also give linear convergence results under a special case of our proposed method. Preliminary numerical results show that our proposed method is competitive with other related methods in the literature.

KEYWORDS:

• Double inertial
• projection methods
• variational inequality
• weak and strong convergence
• linear convergence

2010 MSC CLASSIFICATIONS:

• 47H05
• 47J20
• 47J25
• 65K15
• 90C25

Acknowledgements

The authors are grateful to the associate editor and the two anonymous referees for their insightful comments and suggestions which have improved greatly on the earlier version of the paper.

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Disclosure statement

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

Additional information

Funding

This work was supported by the NSF of China [grant number 12171435].