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

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.