SIAM Journal on Optimization, Volume 31, Issue 2, Page 1380-1409, January 2021.
Metric regularity and a stability theorem with a square-root distance estimate are investigated for smooth mappings which act in Hilbert spaces. The main result concerns a sufficient condition for this type of metric regularity and stability, which is formulated without a priori normality assumptions. As an application of the obtained conditions, Lyusternik's tangent cone theorem and the inverse function theorem in a neighborhood of abnormal point are derived. Examples are constructed which demonstrate the essence of the proposed assumptions.

中文翻译：

---

光滑映射的平方根度量规则和相关稳定性定理

SIAM优化杂志，第31卷，第2期，第1380-1409页，2021年1月。
研究了在希尔伯特空间中起作用的平滑映射的度量规则性和具有平方根距离估计的稳定性定理。主要结果涉及此类度量规则性和稳定性的充分条件，该条件是在没有先验正态性假设的情况下制定的。作为获得条件的应用，推导了异常点附近的Lyusternik切线锥定理和反函数定理。构造了一些例子，这些例子证明了所提出假设的实质。