降维积空间重构下集合的正则性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-20 DOI:10.1007/s11228-023-00702-2

Rubén Campoy

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引用次数: 0

摘要

关于集合的正则性和集合集合的正则性的不同概念在分析非凸情形下投影算法的收敛性时起着重要的作用。虽然一些投影算法可以应用于由有限多个集合定义的可行性问题，但其他一些则需要使用积空间重构来构造具有两个集合的等效问题。在本文中，我们分析了在降维积空间中，一些正则性是如何在重新表述下保持的。这允许我们建立局部线性收敛的平行投影方法，这是构造通过这个重新表述。

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Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.

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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.