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点到凸集的距离函数的凸性证明及其可微性研究

Author(s)：
徐品桑晓勤

Publication Title：

Wen Yuan (Primary School Edition) 2021 No.02

Affiliations：
南阳农业职业学院河南南阳 473000

Abstract：
凸优化理论在应用数学领域中有着重要的应用,点到凸集的距离函数是凸优化理论中的常用概念.本文介绍了点到凸集的距离函数的一些性质,利用凸分析的理论证明了此函数是凸函数.本文引入法锥的概念并结合投影函数的性质,得到了距离函数的次梯度的显示表达式.为了是我们的结论更易理解,我们给出两个算例对主要结论做出说明.

Keywords：
凸集;距离函数;可微性

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[1] 徐品,桑晓勤.点到凸集的距离函数的凸性证明及其可微性研究[J].Wen Yuan (Primary School Edition),2021(02),.

文渊(小学版)

Wen Yuan (Primary School Edition)

Language: 中文

CN：11-9274/G

ISSN：2096-6261

Publication Frequency: 月刊

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