Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential
نویسندگان
چکیده
منابع مشابه
Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential
We prove that uniform second order growth, tilt stability, and strong metric regularity of the subdifferential — three notions that have appeared in entirely different settings — are all essentially equivalent for any lower-semicontinuous, extended-real-valued function.
متن کاملSecond-order Growth, Tilt Stability, and Metric Regularity of the Subdifferential
This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefinite...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملHölder Stable Minimizers, Tilt Stability, and Hölder metric Regularity of Subdifferentials
Using techniques of variational analysis and dual techniques for smooth conjugate functions, for a local minimizer of a proper lower semicontinuous function f on a Banach space, p ∈ (0, +∞) and q = 1+p p , we prove that the following two properties are always equivalent: (i) x̄ is a stable q-order minimizer of f and (ii) x̄ is a tilt-stable p-order minimizer of f . We also consider their relation...
متن کاملStability of p-order metric regularity
This paper shows that p-order metric regularity is preserved under perturbation of Hölder continuous mapping of order 1/p, which answers affirmatively a problem posed recently by Dontchev [2].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2013
ISSN: 1052-6234,1095-7189
DOI: 10.1137/120876551