Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-21 DOI:10.1007/s10957-024-02488-1

Caroline Geiersbach, Tim Suchan, Kathrin Welker

引用次数: 0

Abstract

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.

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黎曼形状芒模中的随机增量拉格朗日法

在本文中，我们提出了一种（可能是无限维的）黎曼流形上的随机增强拉格朗日方法，用于解决带有有限数量确定性约束的随机优化问题。我们对该方法的收敛性进行了研究，该方法基于随机逼近方法，并将随机停止与更新拉格朗日乘数的迭代程序相结合。我们将该算法应用于具有几何约束的多形状优化问题，并进行了数值演示。

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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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.