An inertial-type algorithm for a class of bilevel variational inequalities with the split variational inequality problem constraints

Abstract

In this paper, we investigate the problem of solving strongly monotone variational inequalities over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces and establish a new iterative algorithm for it. Our algorithms are accelerated by the inertial technique and eliminate the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operator by employing a self-adaptive step size criterion. The strong convergence result is given under some mild conditions widely used in the convergence analysis. Two corollaries for the solutions of the split variational inequality problem and the split feasibility problem with multiple output sets are also obtained using our main result. Finally, some numerical experiments have been conducted to illustrate the effectiveness of the proposed algorithms and compare them with the related ones.

Keywords:

• Variational inequality problem
• split variational inequality
• inertial technique
• metric projection
• iterative algorithms

AMS CLASSIFICATIONS:

• 49J40
• 90C33
• 47H10

Acknowledgments

The authors would like to thank the referees and the editor for their valuable comments and suggestions which improve the presentation of this manuscript.

Disclosure statement

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