VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES*

doi:10.1007/s10473-024-0503-6

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1696-1706.doi: 10.1007/s10473-024-0503-6

VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*

Ziyi Zhou, Yi Jiang^†

School of Mathematical Sciences, Visual Computing and Virtual Reality Key Laboratory,Sichuan Normal University, Chengdu 610066, China

收稿日期:2023-03-23 修回日期:2024-05-27 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Yi JIANG, E-mail,: yijiang103@163.com
作者简介:Ziyi Zhou, E-mail,: zhouziyi0713@sina.com
基金资助:
Jiang's research was supported by the National Natural Science Foundation of China (11201324), the Fok Ying Tuny Education Foundation (141114) and the Sichuan Technology Program (2022ZYD0011, 2022NFSC1852).

VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*

Ziyi Zhou, Yi Jiang^†

School of Mathematical Sciences, Visual Computing and Virtual Reality Key Laboratory,Sichuan Normal University, Chengdu 610066, China

Received:2023-03-23 Revised:2024-05-27 Online:2024-10-25 Published:2024-10-22
Contact: †Yi JIANG, E-mail,: yijiang103@163.com
About author:Ziyi Zhou, E-mail,: zhouziyi0713@sina.com
Supported by:
Jiang's research was supported by the National Natural Science Foundation of China (11201324), the Fok Ying Tuny Education Foundation (141114) and the Sichuan Technology Program (2022ZYD0011, 2022NFSC1852).

摘要/Abstract

摘要： 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.

关键词: maximal time function, subdifferential, normal cone, nonsmooth analysis

Abstract: 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.

Key words: maximal time function, subdifferential, normal cone, nonsmooth analysis

中图分类号:

49J50

Ziyi Zhou, Yi Jiang. VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*[J]. 数学物理学报(英文版), 2024, 44(5): 1696-1706.

Ziyi Zhou, Yi Jiang. VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1696-1706.

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VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*

VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES^*

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