Reference : Metric regularity of Newton's iteration
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Metric regularity of Newton's iteration
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Dontchev, A. L. [> >]
Gaydu, M. [> >]
Geoffroy, M.H. [> >]
Veliov, V. M. [> >]
SIAM Journal on Control and Optimization
Yes (verified by ORBilu)
[en] Lyusternik-Graves theorem ; Newton's method ; metric regularity
[en] 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.
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)

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