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.

中文翻译：

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基于道格拉斯-拉奇福德分裂的非凸 ADMM 的安德森加速

交替方向乘法器方法 (ADMM) 广泛用于计算机图形学中，用于解决可能是非光滑和非凸的优化问题。它很快收敛到近似解，但可能需要很长时间才能收敛到高精度解。以前，安德森加速已应用于 ADMM，将其视为对偶变量和原始变量子集串联的定点迭代。在本文中，我们注意到 ADMM 和 Douglas-Rachford 分裂之间的等价性表明 ADMM 实际上是低维空间中的定点迭代。通过将安德森加速应用于这种低维定点迭代，我们获得了一种更有效的加速 ADMM 的方法。我们分析了所提出的加速方法在非凸问题上的收敛性，