SIAM Journal on Optimization, Volume 30, Issue 4, Page 3170-3197, January 2020.
We consider the application of the type-I Anderson acceleration to solving general nonsmooth fixed-point problems. By interleaving with safeguarding steps and employing a Powell-type regularization and a restart checking for strong linear independence of the updates, we propose the first globally convergent variant of Anderson acceleration assuming only that the fixed-point iteration is nonexpansive. We show by extensive numerical experiments that many first order algorithms can be improved, especially in their terminal convergence, with the proposed algorithm. Our proposed method of acceleration is being implemented in SCS 2.1, one of the default solvers used in the convex optimization parser-solver CVXPY 1.0.

中文翻译：

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非光滑定点迭代的全局收敛的I类安德森加速

SIAM优化杂志，第30卷，第4期，第3170-3197页，2020年1月。
我们考虑将I型安德森加速器用于解决一般的非光滑定点问题。通过与保护步骤进行交织并采用Powell型正则化和重新启动检查以确保更新具有很强的线性独立性，我们提出了第一个Anderson加速的全局收敛变体，仅假设定点迭代是非扩展的。通过大量的数值实验，我们证明了所提出的算法可以改善许多一阶算法，特别是在它们的终端收敛方面。我们提出的加速方法正在SCS 2.1中实现，SCS 2.1是凸优化分析器-求解器CVXPY 1.0中使用的默认求解器之一。