Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
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DOI：
10.1137/090772174
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发表时间：
2010-04
期刊：
影响因子：
--
通讯作者：
Xi Yin Zheng;K. Ng
中科院分区：
文献类型：
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作者：
Xi Yin Zheng;K. Ng
本文讨论了Banach空间之间由闭集函数定义的广义方程，利用变分分析方法给出了广义方程具有度量次正则性的充分必要条件（即，局部误差界）。按照Ioffe [Trans. Amer. Math. Soc.，251（1979），pp. 61-69]研究了数值函数的情况，我们的条件被描述为在解集之外的点处的相关多功能的余导数。受现有度量正则性的模表示和基于点的度量正则性准则的启发，我们建立了度量次正则性的相应结果。在Asplund空间的情况下，得到了更尖锐的结果。
This paper concerns a generalized equation defined by a closed multifunction between Banach spaces, and we employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity (i.e., local error bounds for the concerned multifunction) in general Banach spaces. Following the approach of Ioffe [Trans. Amer. Math. Soc., 251 (1979), pp. 61-69] who studied the numerical function case, our conditions are described in terms of coderivatives of the concerned multifunction at points outside the solution set. Motivated by the existing modulus representation and point-based criteria for the metric regularity, we establish the corresponding results for the metric subregularity. In the Asplund space case, sharper results are obtained.