Characterizations of the Strong Basic Constraint Qualifications
Characterizations of the Strong Basic Constraint Qualifications
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DOI：
10.1287/moor.1050.0154
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
Hui Hu
中科院分区：
文献类型：
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作者：
Hui Hu
本文刻画了强基本约束限定(BCQ)与强基本约束限定(BCQ)的一般区别。为此，我们引入了次微分的幅度这一新的度量，证明了对于由真凸函数f定义的一个不等式，解集的边界点x处的强BCQ等价于广义BCQ加上x处次微分幅度的正性。将上述刻画应用于f是有限多个可微凸函数的极大值的情形，我们证明了边界点x处的度量正则性等价于x的“边界邻域”中每一点的BCQ。此外，我们还回答了郑Ng[11]提出的一个公开问题。我们构造了一个例子来说明边界点x处的BCQ不能保证x处的度量正则性。
In this paper, we characterize the general difference between strong basic constraint qualification (BCQ) and BCQ. For this purpose, we introduce a new measurement, the extent of a subdifferential, and show that for an inequality defined by a proper convex function f, the strong BCQ at a boundary point x of the solution set is equivalent to the extended BCQ plus the positivity of the extent of subdifferential at x. Applying the above characterization to the case when f is the maximum of finitely many differentiable convex functions, we show that the metric regularity at a boundary point x is equivalent to BCQ at every point in a "boundary-neighborhood" of x. In addition, we provide an answer to the open question proposed by Zheng and Ng [11]. We construct an example to show that BCQ at a boundary point x does not ensure the metric regularity at x.