Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting

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

Geometric Modeling and Processing mathscidoc:2012.16004

Computer Graphics Forum (Symposium on Geometry Processing), 39, (5), 2020.8
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 including geometry processing and physical simulation.
Solvers, mathematical optimization, numerical analysis
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@inproceedings{wenqing2020anderson,
  title={Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting},
  author={Wenqing Ouyang, Yue Peng, Yuxin Yao, Juyong Zhang, and Bailin Deng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227195920975138731},
  booktitle={Computer Graphics Forum (Symposium on Geometry Processing)},
  volume={39},
  number={5},
  year={2020},
}
Wenqing Ouyang, Yue Peng, Yuxin Yao, Juyong Zhang, and Bailin Deng. Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting. 2020. Vol. 39. In Computer Graphics Forum (Symposium on Geometry Processing). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227195920975138731.
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