A Notion of Fenchel Conjugate for Set-Valued Mappings

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-28 DOI:10.1007/s10957-024-02455-w

Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu, Nguyen Dong Yen

引用次数: 0

Abstract

In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing some fundamental properties of the Fenchel conjugate for set-valued mappings, we derive its main calculus rules in various settings. Our approach is geometric and draws inspiration from the successful application of this method by B.S. Mordukhovich and coauthors in variational and convex analysis. Subsequently, we demonstrate that our new findings for the Fenchel conjugate of set-valued mappings can be utilized to obtain many old and new calculus rules of convex generalized differentiation in both finite and infinite dimensions.

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定值映射的芬切尔共轭概念

在本文中，我们提出了一个新颖的概念，即定值映射的芬切尔共轭，并研究了它在有限维度和无限维度中的性质。在确定了定值映射的 Fenchel 共轭的一些基本性质后，我们推导出了它在各种情况下的主要微积分规则。我们的方法是几何方法，并从 B.S. Mordukhovich 及其合作者在变分和凸分析中成功应用该方法中获得灵感。随后，我们证明了我们对定值映射的芬切尔共轭的新发现可以用来获得有限维度和无限维度凸泛微分的许多新旧微积分规则。

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.