  We consider the application of the type-I Anderson acceleration to solving
general non-smooth fixed-point problems. By interleaving with safe-guarding
steps, and employing a Powell-type regularization and a re-start checking for
strong linear independence of the updates, we propose the first globally
convergent variant of Anderson acceleration assuming only that the fixed-point
iteration is non-expansive. We show by extensive numerical experiments that
many first order algorithms can be improved, especially in their terminal
convergence, with the proposed algorithm. Our proposed method of acceleration
is being implemented in SCS 2.0, one of the default solvers used in the convex
optimization parser-solver CVXPY 1.0.
