We consider the application of the type-I Anderson acceleration to solving
general non-smooth fixed-point problems. By interleaving with safe-guarding
steps, and employing a Powell-type regularization and a re-start 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 non-expansive. 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 2.0, one of the default solvers used in the convex
optimization parser-solver CVXPY 1.0.

本文介绍了第一型 Anderson 加速在求解非光滑的固定点问题中的应用。通过交替使用保护步骤，采用 Powell 类型的正则化和重新启动检查强线性独立性更新，提出了第一个全局收敛的 Anderson 加速变体，假设固定点迭代是非扩张的。通过广泛的数值实验表明，许多一阶算法可以通过所提出的算法进行改进，特别是在终端收敛方面。本文所提出的加速方法正在 SCS 2.0 中得到实现，它是凸优化解析器求解器 CVXPY 1.0 中使用的默认求解器之一。