On error bounds for lower semicontinuous functions
On error bounds for lower semicontinuous functions
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DOI：
10.1007/s101070100278
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发表时间：
2002-04
影响因子：
2.7
通讯作者：
Zili Wu;J. Ye
中科院分区：
文献类型：
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作者：
Zili Wu;J. Ye
我们给出了度量空间上适当的下半连续函数具有误差界限（带指数）的一些充分条件。对于赋范空间上的真凸函数，局部误差界的存在意味着全局误差界的存在。另外如果X是Banach空间，则误差界可以用次微分off来表征。在自反Banach spaceX中，我们进一步得到了Dini下导数off存在误差界的几个充分必要条件。
We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex functionfon a normed spaceXthe existence of a local error bound implies that of a global error bound. If in additionXis a Banach space, then error bounds can be characterized by the subdifferential off. In a reflexive Banach spaceX, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative off.