A golden ratio self-adaptive algorithm for solving a quasimonotone variational inequality in banach spaces

Abstract In this paper, we propose and study a self-adaptive iterative method using golden ratio technique for solving variational inequality problem. We use Lyapunov functional to solve the underlying problem in a 2-uniformly convex Banach space. We obtain a weak convergence result when the cost operator is quasimonotone and locally Lipschitz continuous. Finally, we present numerical experiments to illustrate the applicability of our method. Our method extends some results in this direction in the literature.