论文标题
几乎线性收敛的一阶方法，用于非平滑函数，具有二次生长
A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth
论文作者
论文摘要
经典结果表明，梯度下降线性收敛到平滑强烈凸功能的最小化器。一个自然的问题是，是否存在一种局部几乎线性收敛的方法，用于非平滑函数具有二次生长。这项工作设计了一种方法，用于广泛的非滑动和非凸的本地Lipschitz函数，包括最大平滑的，Shapiro的可分解类别以及通用的半gebraic函数。该算法是无参数的，并源自Goldstein的概念性亚级别方法。
Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linearly convergent method for nonsmooth functions with quadratic growth. This work designs such a method for a wide class of nonsmooth and nonconvex locally Lipschitz functions, including max-of-smooth, Shapiro's decomposable class, and generic semialgebraic functions. The algorithm is parameter-free and derives from Goldstein's conceptual subgradient method.
