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The alternating direction multiplier method (ADMM) is widely used in computergraphics for solving optimization problems that can be nonsmooth and nonconvex.It converges quickly to an approximate solution, but can take a long time toconverge to a solution of high-accuracy. Previously, Anderson acceleration hasbeen applied to ADMM, by treating it as a fixed-point iteration for theconcatenation of the dual variables and a subset of the primal variables. Inthis paper, we note that the equivalence between ADMM and Douglas-Rachfordsplitting reveals that ADMM is in fact a fixed-point iteration in alower-dimensional space. By applying Anderson acceleration to suchlower-dimensional fixed-point iteration, we obtain a more effective approachfor accelerating ADMM. We analyze the convergence of the proposed accelerationmethod on nonconvex problems, and verify its effectiveness on a variety ofcomputer graphics problems including geometry processing and physicalsimulation.

Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting