A Newton iteration for differentiable set-valued maps

We employ recent developments of generalized differentiation concepts for set-valued mappings and present a Newton-like iteration for solving generalized equations of the form f(x)+F(x)∋0 where f is a single-valued function while F stands for a set-valued map, both of them being smooth mappings acti...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 399; no. 1; pp. 213 - 224
Main Authors Gaydu, Michaël, Geoffroy, Michel H.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2013
Elsevier
Subjects
[formula omitted]-differentiability
Positively homogeneous mappings
Successive approximations
Variational inclusions
H-differentiability
Successive approximations
Variational inclusions
Positively homogeneous mappings
Online AccessGet full text

Cover

More Information
Summary:We employ recent developments of generalized differentiation concepts for set-valued mappings and present a Newton-like iteration for solving generalized equations of the form f(x)+F(x)∋0 where f is a single-valued function while F stands for a set-valued map, both of them being smooth mappings acting between two general Banach spaces X and Y. The Newton iteration we propose is constructed on the basis of a linearization of both f and F; we prove that, under suitable assumptions on the “derivatives” of f and F, it converges Q-linearly to a solution to the generalized equation in question. When we strengthen our assumptions, we obtain the Q-quadratic convergence of the method.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.10.012