  The Douglas-Rachford method is a popular splitting technique for finding a
zero of the sum of two subdifferential operators of proper closed convex
functions; more generally two maximally monotone operators. Recent results
concerned with linear rates of convergence of the method require additional
properties of the underlying monotone operators, such as strong monotonicity
and cocoercivity. In this paper, we study the case when one operator is
Lipschitz continuous but not necessarily a subdifferential operator and the
other operator is strongly monotone. This situation arises in optimization
methods which involve primal-dual approaches. We provide new linear convergence
results in this setting.
