Metric Regularity and Constraint Qualifications for Convex Inequalities on Banach Spaces
Metric Regularity and Constraint Qualifications for Convex Inequalities on Banach Spaces
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DOI：
10.1137/s1052623403423102
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发表时间：
2003-03
期刊：
影响因子：
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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
我们引入了扩展基本约束资格和强基本约束资格的新概念，并讨论了它们与基本约束资格和度量正则性等基本概念的关系;特别地，我们解决了刘易斯和庞的一个公开问题：用正规锥刻画度量正则性.利用强基本约束条件给出了凸不等式误差界的一个刻画。作为应用，我们研究了Banach空间中闭凸集的无限集合的线性正则性。
We introduce new notions of the extended basic constraint qualification and the strong basic constraint qualification and discuss their relationship with other fundamental concepts such as the basic constraint qualification and the metric regularity; in particular we provide a solution to an open problem of Lewis and Pang on characterizing the metric regularity in terms of normal cones. We present a characterization of error bounds for convex inequalities in terms of the strong basic constraint qualification. As applications, we study the linear regularity for infinite collections of closed convex sets in a Banach space.