Linearized Douglas–Rachford method for variational inequalities with Lipschitz mappings.

In this article, we introduce linearized Douglas–Rachford method for solving Lipschitz continuous variational inequalities in Hilbert space. First, we show the linear convergence of linearized Douglas–Rachford method with the fixed stepsize for the strongly monotone mapping. The usual drawback of algorithms with the fixed stepsize is the requirement to know the Lipschitz constant of the mapping. To avoid this, we present linearized Douglas–Rachford method with the diminishing stepsize whose convergence is established for the strongly pseudomonotone mapping. Finally, preliminary results from numerical experiments are promising. [ABSTRACT FROM AUTHOR]