  The alternating direction multiplier method (ADMM) is widely used in computer
graphics for solving optimization problems that can be nonsmooth and nonconvex.
It converges quickly to an approximate solution, but can take a long time to
converge to a solution of high-accuracy. Previously, Anderson acceleration has
been applied to ADMM, by treating it as a fixed-point iteration for the
concatenation of the dual variables and a subset of the primal variables. In
this paper, we note that the equivalence between ADMM and Douglas-Rachford
splitting reveals that ADMM is in fact a fixed-point iteration in a
lower-dimensional space. By applying Anderson acceleration to such
lower-dimensional fixed-point iteration, we obtain a more effective approach
for accelerating ADMM. We analyze the convergence of the proposed acceleration
method on nonconvex problems, and verify its effectiveness on a variety of
computer graphics problems including geometry processing and physical
simulation.
