非光滑映射通过最速位移率的强度量次正则分析
A strong metric subregularity analysis of nonsmooth mappings via steepest displacement rate
摘要：
本文利用变分工具最速位移率，系统地研究了映射的强度量次正则性。借助于这一工具，给出了作用在度量空间上的集值集的强度量次正则性的一个简单刻画。由此产生的标准是有用的强度量次正则性的扰动的存在下，以及用于推导各种条件，使检测这样的属性的情况下，非光滑映射的稳定性。其中的一些条件，涉及几个非光滑分析的建设，然后应用于研究的孤立冷静性质的解决方案映射到参数化的广义方程。
英文摘要：
In this paper, a systematic study of the strong metric subregularity property of mappings is carried out by means of a variational tool, called steepest displacement rate. With the aid of this tool, a simple characterization of strong metric subregularity for multifunctions acting in metric spaces is formulated. The resulting criterion is shown to be useful for establishing stability properties of the strong metric subregularity in the presence of perturbations, as well as for deriving various conditions, enabling to detect such a property in the case of nonsmooth mappings. Some of these conditions, involving several nonsmooth analysis constructions, are then applied in studying the isolated calmness property of the solution mapping to parameterized generalized equations.
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