Square-Root Metric Regularity and Related Stability Theorems for Smooth Mappings
Aram Vladimirovich Arutyunov, Dmitry Yu. Karamzin · SIAM Journal on Optimization · 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.