A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems

ABSTRACT

In this paper, we propose a single projection method for finding a solution of the bilevel pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm requires only one projection onto the feasible set. Also, we prove strong convergence theorems of the proposed method under mild conditions, which improve some related results in the literature. Finally, we present some numerical experiments to show the efficiency and advantages of the proposed algorithm.

Keywords:

• Contraction and projection method
• bilevel variational inequality problem
• pseudo-monotone mapping

2010 Mathematics Subject Classifications:

• 47H09
• 47J20
• 47J05
• 47J25

Acknowledgments

The authors would like to thank the two referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper.

Disclosure statement

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