基于共轭的凸上影线的$\varepsilon $次微分方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-03-12 DOI:10.1007/s11228-024-00712-8

Rafael Correa, Abderrahim Hantoute, Marco A. López

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引用次数: 0

摘要

我们为任意凸函数族的上确界的（（varepsilon \）-次微分提供了新的特征。由此得到的公式只涉及数据函数的适当凸组合的近似次微分。介绍了具有类似凹凸性质的凸函数族，并研究了它们与仿射模型的关系。还分析了数据函数的下半连续性的作用。

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Conjugation-Based Approach to the $\varepsilon $ -Subdifferential of Convex Suprema

We provide new characterizations of the $\varepsilon $-subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.

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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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