关于非平滑优化中确定性梯度采样收敛性的说明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-02-06 DOI:10.1007/s10589-024-00552-0

Bennet Gebken

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引用次数: 0

摘要

在计算非光滑优化问题的下降方向时，近似子微分是主要任务之一。在本文中，我们提出了一种针对弱下半滑函数的二分法，该方法能够计算新的子梯度，从而在计算的下降方向不充分的情况下改进给定的近似值。结合最近提出的确定性梯度采样方法，这将产生一种确定性的、可证明收敛的近似子微分方法，用于计算下降方向。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A note on the convergence of deterministic gradient sampling in nonsmooth optimization

Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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