Error Bounds for Lower Semicontinuous Functions in Normed Spaces
Error Bounds for Lower Semicontinuous Functions in Normed Spaces
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DOI：
10.1137/s1052623499358884
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
K. Ng;Xi Yin Zheng
中科院分区：
文献类型：
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作者：
K. Ng;Xi Yin Zheng
在不考虑凸性和可解析性假设的情况下，研究了由一般下半连续函数定义的不等式系统的误差界，建立了无穷维赋范空间中误差界存在的充要条件。给出了在自反巴拿赫空间中具有误差界的凸不等式系统的一些刻画。作为应用，在处理赋范空间中的Hoffman误差界结果时，我们给出了一个可计算的Lipschitz界常数，在某些例子中优于以往的Lipschitz界常数；我们还考虑了Rn上二次函数的误差界。
Without the convexity or analyticity assumption, we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient/necessary conditions on the existence of error bounds in infinite dimensional normed spaces. Some characterizations for a convex inequality system to possess an error bound in a reflexive Banach space are also given. As applications, in dealing with the Hoffman error bound result in normed spaces, we give a computable Lipschitz bound constant, which is better than previous Lipschitz bound constants in some examples; we also consider error bounds for quadratic functions on Rn.