1. What are the contributions in "Anderson acceleration for nonconvex admm" ?
In this paper, the authors 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.. The authors 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.. This is the accepted version of the following article: Ouyang, W., Peng, Y., Yao, Y., Zhang, J. and Deng, B. ( 2020 ), Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting.. This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy.
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2. What is the way to improve stability?
To improve stability, in [ZPOD19] an accelerated iterate is accepted only if it decreases a certain quantity that will converge to zero with effective iterations, such as the combined residual.
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3. What is the common type of proximal splitting methods?
One example of such proximal splitting methods is the local-global solvers commonly used for geometry processing and physical simulation [SA07, LZX∗08, BDS∗12, LBOK13, BML∗14].
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4. How does the acceleration technique speed up convergence of the steps?
By treating the steps (2)–(4) as a fixed-point iteration of the variables (x,y) , it speeds up the convergence using Anderson acceleration [And65], a well-known acceleration technique for fixedpoint iterations.
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![Figure 6: Comparison on a convex problem (41) with λ = 2, for computing local mesh deformation components from an input mesh sequence and given weights. The methods are tested using two mesh sequences constructed from the facial expression dataset of [RBSB18], with 100 frames and 250 frames, respectively. We set the penalty parameter to β = 10 for both problem instances. Our method have similar acceleration performance as AA-ADMM in reducing the number of iterations, and outperforms AA-ADMM in actual computational time.](/figures/figure-6-comparison-on-a-convex-problem-41-with-l-2-for-3o5cm47h.webp)
![Figure 8: Comparison on the ADMM solver in [TZD∗19] for recovering geodesic distance on meshes. Both AA-ADMM and our method can reduce the number of iterations required for convergence, but their actual computational time is higher due to the very low computational cost per iteration for the ADMM solver. Our method takes a shorter time than AA-ADMM thanks to its lower overhead.](/figures/figure-8-comparison-on-the-admm-solver-in-tzd-19-for-x641vcsq.webp)
