Accelerating ADMM for Efficient Simulation and Optimization

Juyong Zhang University of Science and Technology of China Yue Peng University of Science and Technology of China Wenqing Ouyang University of Science and Technology of China Bailin Deng Cardiff University

Geometric Modeling and Processing mathscidoc:2012.16003

ACM Transactions on Graphics (SIGGRAPH Asia), 38, (6), 163, 2019.11
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.
Physics Simulation, Geometry Optimization, ADMM, Anderson Acceleration
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@inproceedings{juyong2019accelerating,
  title={Accelerating ADMM for Efficient Simulation and Optimization},
  author={Juyong Zhang, Yue Peng, Wenqing Ouyang, and Bailin Deng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227193605800817730},
  booktitle={ACM Transactions on Graphics (SIGGRAPH Asia)},
  volume={38},
  number={6},
  pages={163},
  year={2019},
}
Juyong Zhang, Yue Peng, Wenqing Ouyang, and Bailin Deng. Accelerating ADMM for Efficient Simulation and Optimization. 2019. Vol. 38. In ACM Transactions on Graphics (SIGGRAPH Asia). pp.163. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227193605800817730.
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