  Anderson acceleration is a well-established and simple technique for speeding
up fixed-point computations with countless applications. Previous studies of
Anderson acceleration in optimization have only been able to provide
convergence guarantees for unconstrained and smooth problems. This work
introduces novel methods for adapting Anderson acceleration to (non-smooth and
constrained) proximal gradient algorithms. Under some technical conditions, we
extend the existing local convergence results of Anderson acceleration for
smooth fixed-point mappings to the proposed scheme. We also prove analytically
that it is not, in general, possible to guarantee global convergence of native
Anderson acceleration. We therefore propose a simple scheme for stabilization
that combines the global worst-case guarantees of proximal gradient methods
with the local adaptation and practical speed-up of Anderson acceleration.
