Iterative solving of generalized equations with calm solution mappings

We present an iterative procedure for solving, in finite dimensions, generalized equations of the form (∗) 0 ∈ f ( x ) + F ( x ) , where f is a continuous function while F stands for a closed set-valued mapping. Assuming that f belongs to a class of functions admitting a certain type of approximatio...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2006, Vol.313 (2), p.689-699
Main Author: Geoffroy, Michel H.
Format: Article
Language:English
Subjects:
Calmness
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Real functions
Sciences and techniques of general use
Set-valued mappings
Superlinear convergence
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Summary:We present an iterative procedure for solving, in finite dimensions, generalized equations of the form (∗) 0 ∈ f ( x ) + F ( x ) , where f is a continuous function while F stands for a closed set-valued mapping. Assuming that f belongs to a class of functions admitting a certain type of approximation and that the solution set of (∗) satisfies a calmness-type property we show that the method we consider is superlinearly convergent to a solution of (∗).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.06.070