Two novel two-step inertial algorithms for a class of bilevel variational inequalities

Abstract

This paper introduces two novel two-step inertial and self-adaptive step sizes algorithms for solving a strongly monotone variational inequality over the solution set of a split convex feasibility problem with multiple output sets in real Hilbert spaces. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve monotone variational inequalities over the solution set of the split feasibility problem. The method is further applied to the image classification problem via the support vector machine learning. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature.

Keywords:

• Hilbert spaces
• variational inequality
• split convex feasibility problem
• strong convergence
• inertial term

AMS SUBJECT 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. The authors contributed equally to this work.

Data availability

The MNIST dataset that supports the findings of this study is available from https://cs.nyu.edu/%7Eroweis/data.html

Disclosure statement

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