Modified inertial projection methods for bilevel quasi-monotone variational inequalities

Abstract

In this paper, we propose two projection-based methods with different inertial steps to solve the bilevel quasi-monotone variational inequality problem in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration with Armijo line search methods. Strong convergence theorems of the proposed algorithms are established under some suitable and mild conditions. Some numerical examples are given to illustrate the comparison of our proposed algorithms with some already known algorithms.