Various Lipschitz-like Properties for Functions and Sets I: Directional Derivative and Tangential Characterizations | Zendy

Rafaël Correa | Zendy; Pedro Gajardo | Zendy; Lionel Thibault | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Various Lipschitz-like Properties for Functions and Sets I: Directional Derivative and Tangential Characterizations

Author(s) -

Rafaël Correa,

Pedro Gajardo,

Lionel Thibault

Publication year - 2010

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/080738271

Subject(s) - mathematics , lipschitz continuity , banach space , tangent cone , directional derivative , bounded function , tangent , pure mathematics , regular polygon , zero (linguistics) , space (punctuation) , mathematical analysis , discrete mathematics , geometry , linguistics , philosophy

In this work we introduce for extended real valued functions, defined on a Banach space X, the concept of K directionally Lipschitzian behavior, where K is a bounded subset of X. For different types of sets K (e.g., zero, singleton, or compact), the K directionally Lipschitzian behavior recovers well-known concepts in variational analysis (locally Lipschitzian, directionally Lipschitzian, or compactly epi-Lipschitzian properties, respectively). Characterizations of this notion are provided in terms of the lower Dini subderivatives. We also adapt the concept for sets and establish characterizations of the mentioned behavior in terms of the Bouligand tangent cones. The special case of convex functions and sets is also studied.This research was partially supported by FONDECYT project 1080173 and Programa Basal CMM U. de Chile

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research