VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES*

doi:10.1007/s10473-024-0503-6

Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (5): 1696-1706.doi: 10.1007/s10473-024-0503-6

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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).

Abstract

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

CLC Number:

49J50

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^*

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