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Anderson acceleration for nonconvex ADMM based on Douglas-Rachford splitting

Ouyang, Wenqing, Peng, Yue, Yao, Yuxin, Zhang, Juyong and Deng, Bailin 2020. Anderson acceleration for nonconvex ADMM based on Douglas-Rachford splitting. Computer Graphics Forum 39 (5) , pp. 221-239.
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Abstract

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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Publisher: Wiley
ISSN: 0167-7055
Date of First Compliant Deposit: 25 June 2020
Date of Acceptance: 23 June 2020
Last Modified: 10 Sep 2020 11:25
URI: http://orca.cf.ac.uk/id/eprint/132807

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