An extragradient method with conjugate gradient-type direction for solving variational inequalities with application

Abstract.

In this paper, we establish a fact that guarantees the strong convergence of any sequence of images of a metric projection onto a closed convex set . We further incorporated the extragradient technique with a conjugate gradient-type direction to solve monotone variational inequality problems in Hilbert spaces. Unlike existing conjugate gradient-type methods, the proposed method does not require boundedness of the feasible set to converge to a solution of the variational inequality problem. In this regard, we establish weak convergence for the proposed method under appropriate conditions and conduct numerical experiments to showcase the computational efficacy and robustness of the method. Finally, we illustrate a potential application of the method in solving international migration equilibrium problem.