规范空间中最大时间函数的变量分析

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0503-6

Ziyi Zhou, Yi Jiang

{"title":"规范空间中最大时间函数的变量分析","authors":"Ziyi Zhou, Yi Jiang","doi":"10.1007/s10473-024-0503-6","DOIUrl":null,"url":null,"abstract":"<p>For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"26 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Variational analysis for the maximal time function in normed spaces\",\"authors\":\"Ziyi Zhou, Yi Jiang\",\"doi\":\"10.1007/s10473-024-0503-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.</p>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0503-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0503-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于一般的规范向量空间，我们考虑了一种特殊的最优值函数，称为最大时间函数。它涵盖了作为特例的最远距离函数，并与最小包围球问题有密切关系。本文证明了最大时间函数的一些性质，包括凸性、下半连续性及其子微分公式的精确特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Variational analysis for the maximal time function in normed spaces

For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.