| 赋范线性空间中最小时间函数的ε-次微分 |
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| 引用本文： | 孙淑芹,何诣然,刘军.赋范线性空间中最小时间函数的ε-次微分[J].数学学报,2018,61(3):485-496. |
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| 作者姓名： | 孙淑芹 何诣然 刘军 |
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| 作者单位： | 1.西华师范大学数学与信息学院 南充 637002;2.四川师范大学数学与软件科学学院 成都 610066 |
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| 基金项目： | 国家自然科学基金资助项目（11271274，11461058）；西华师范大学博士科研启动基金项目 |
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| 摘 要： | 在赋范线性空间中，本文讨论最小时间函数TS的ε次微分计算公式.TS由非空闭集S和非空闭凸集U决定，并以距离函数和指示函数为其特例.本文利用新的讨论方法取消了已有结果中的重要假设：TS满足calmness条件，建立了TS在集合S外的点处的ε-次微分的下估计式，该估计式由相应的法锥和集合U的支撑函数的次水平集表示.
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ε-subdifferential of the Minimal Time Function in Normed Vector Space |
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| Shu Qin SUN,Yi Ran HE,Jun LIU.ε-subdifferential of the Minimal Time Function in Normed Vector Space[J].Acta Mathematica Sinica,2018,61(3):485-496. |
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| Authors: | Shu Qin SUN Yi Ran HE Jun LIU |
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| Institution: | 1.School of Mathematics and Information, China West Normal University, Nanchong 637002, P. R. China;2.Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China |
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| Abstract: | In a normed vector space, we study the ε-subdifferential of the minimal time function TS which is determined by a closed set S and a bounded closed convex set U. TS covers distance function and indicator function as special cases. Without calmness assumption on TS, which is required in the known results in the literature, a new argument is used to obtain the lower estimates for ε-subdifferential of TS at points outside S being representable by virtue of the appropriate normal cones and the sublevel sets of the support function of U. |
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| Keywords: | minimal time function normal cone ε-subdifferential |
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