Implicit function theorems for generalized equations |
| |
Authors: | Asen L. Dontchev |
| |
Affiliation: | (1) Mathematical Reviews, 416 Fourth Street, P.O. Box 8604, 48107-8604 Ann Arbor, MI, USA |
| |
Abstract: | We show that Lipschitz and differentiability properties of a solution to a parameterized generalized equation 0 f(x, y) + F(x), wheref is a function andF is a set-valued map acting in Banach spaces, are determined by the corresponding Lipschitz and differentiability properties of a solution toz g(x) + F(x), whereg strongly approximatesf in the sense of Robinson. In particular, the inverse map (f + F)–1 has a local selection which is Lipschitz continuous nearx0 and Fréchet (Gateaux, Bouligand, directionally) differentiable atx0 if and only if the linearization inverse (f (x0) + f (x0) (× – x0) + F(×))–1 has the same properties. As an application, we study directional differentiability of a solution to a variational inequality.This work was supported by National Science Foundation Grant Number DMS 9404431. |
| |
Keywords: | Generalized equations Implicit function theorems Sensitivity Variational inequality |
本文献已被 SpringerLink 等数据库收录! |
|