Douglas-Rachford splitting algorithm for projected solution of quasi variational inequality with non-self constraint map

Abstract In this paper, we present a Douglas-Rachford splitting algorithm within a Hilbert space framework that yields a projected solution for a quasi-variational inequality. This is achieved under the conditions that the operator associated with the problem is Lipschitz continuous and strongly monotone. The proposed algorithm is based on the interaction between the resolvent operator and the reflected resolvent operator.