具有二次增长的非光滑函数的局部近线性收敛一阶方法

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2024-06-14 DOI:10.1007/s10208-024-09653-y

Damek Davis, Liwei Jiang

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引用次数: 0

摘要

经典结果表明，梯度下降线性收敛于光滑强凸函数的最小值。一个自然的问题是，对于二次增长的非光滑函数，是否存在一种近乎线性收敛的局部方法。这项研究为一大类非光滑和非凸局部 Lipschitz 函数设计了这样一种方法，包括最大光滑函数、Shapiro 的可分解类函数和一般半代数函数。该算法无参数，源自戈尔茨坦的概念子梯度法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Local Nearly Linearly Convergent First-Order Method for Nonsmooth Functions with Quadratic Growth

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A Local Nearly Linearly Convergent First-Order Method for Nonsmooth Functions with Quadratic Growth

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.

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.