Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting [article]

Wenqing Ouyang and Yue Peng and Yuxin Yao and Juyong Zhang and Bailin Deng
2020 arXiv   pre-print
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
more » ... nce 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.
arXiv:2006.14539v2 fatcat:wci4nih6ybfmpl3ko376iyuyqi