Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators

Abstract

In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.