论文标题
寻求规律性理论中简单而统一的证据：扰动稳定性
A Quest for Simple and Unified Proofs in Regularity Theory: Perturbation Stability
论文作者
论文摘要
Ioffe的标准及其对其进行了各种重新制定已成为证明定理的标准工具，可以保证（设置值）映射的度量规则。首先，我们证明人们应始终直接使用所谓的一般标准，例如，从Ekeland的各种原理中，并且无需通过此一般性陈述的基于斜率的后果进行绕行。其次，我们认为，在证明扰动稳定性的情况下，本着lyusternik-graves定理的精神，即使在目标空间不完整的情况下，也无需采用较低的半连续信封的概念。要旨是使用应用Ekeland的变分原理的“正确”功能；也就是说，所考虑的设置值映射的距离函数。这种方法起源于L. thibault引入的图形规律性的概念，这等同于公制规则性的属性。我们的标准涵盖了度量次数和度量半牙，这是通过固定度量规则定义中的一个点之一获得的弱性能。
Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing metric regularity of a (set-valued) mapping. First, we demonstrate that one should always use directly the so-called general criterion which follows, for example, from Ekeland's variational principle, and that there is no need to make a detour through the slope-based consequences of this general statement. Second, we argue that when proving perturbation stability results, in the spirit of Lyusternik-Graves theorem, there is no need to employ the concept of a lower semi-continuous envelope even in the case of an incomplete target space. The gist is to use the "correct" function to which Ekeland's variational principle is applied; namely, the distance function to the graph of the set-valued mapping under consideration. This approach originates in the notion of graphical regularity introduced by L. Thibault, which is equivalent to the property of metric regularity. Our criteria cover also both metric subregularity and metric semiregularity, which are weaker properties obtained by fixing one of the points in the definition of metric regularity.
