  We consider the problem of non-smooth convex optimization with linear
equality constraints, where the objective function is only accessible through
its proximal operator. This problem arises in many different fields such as
statistical learning, computational imaging, telecommunications, and optimal
control. To solve it, we propose an Anderson accelerated Douglas-Rachford
splitting (A2DR) algorithm, which we show either globally converges or provides
a certificate of infeasibility/unboundedness under very mild conditions.
Applied to a block separable objective, A2DR partially decouples so that its
steps may be carried out in parallel, yielding an algorithm that is fast and
scalable to multiple processors. We describe an open-source implementation and
demonstrate its performance on a wide range of examples.
