GLOBALLY CONVERGENT TYPE-I ANDERSON ACCELERATION FOR NONSMOOTH FIXED-POINT ITERATIONS

摘要

We consider the application of the type-I Anderson acceleration to solving general nonsmooth fixed-point problems. By interleaving with safeguarding steps and employing a Powell-type regularization and a restart 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 nonexpansive. 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 2.1, one of the default solvers used in the convex optimization parser-solver CVXPY 1.0.