Aragón Artacho, Francisco Javier, Dontchev, Asen L., Gaydu, Michaël, Geoffroy, Michel H., Veliov, Vladimir M.
Metric regularity of Newton's iteration
ARAGÓN ARTACHO, F.J., et al. "Metric regularity of Newton's iteration". SIAM Journal on Control and Optimization. Vol. 49, No. 2 (2011). ISSN 0363-0129, pp. 339-362
URI: http://hdl.handle.net/10045/29036
DOI: 10.1137/100792585
ISSN: 0363-0129 (Print)
Abstract: 
For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik–Graves theorem to the framework of a mapping acting from the pair “parameter-starting point” to the set of corresponding convergent Newton sequences. Under ample parameterization, metric regularity of the mapping associated with convergent Newton sequences becomes equivalent to the metric regularity of the mapping associated with the generalized equation. We also discuss an inexact Newton method and present an application to discretized optimal control.
Keywords:Lyusternik-Graves theorem, Newton’s method, Generalized equation, Metric regularity, Perturbations, Optimal control
Society for Industrial and Applied Mathematics (SIAM)
info:eu-repo/semantics/article