A projection-fixed point method for a class of bilevel variational inequalities with split fixed point constraints

Abstract

We propose a method for solving bilevel split variational inequalities involving strongly monotone operators in the leader problems and nonexpansive mappings in the follower ones. The proposed method is a combination between the projection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. Strong convergence of the iterative process is proved. Special cases are considered.

Keywords:

• split feasibility problem
• bilevel variational inequality
• Krasnoselskii–Mann scheme
• projection method
• nonexpansive mapping

AMS Subject Classifications:

• 47J25
• 47N10
• 90C25

Acknowledgements

We would like to thank the referees for their useful remarks and comments that helped us very much in revising the paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of second author was supported by the NAFOSTED, Vietnam.