Newton’s method for generalized equations: a sequential implicit function theorem

In an extension of Newton’s method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton’s iterates as elements of a sequence space...

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Vydáno v:	Mathematical programming Ročník 123; číslo 1; s. 139 - 159
Hlavní autoři:	Dontchev, A. L., Rockafellar, R. T.
Médium:	Journal Article Konferenční příspěvek
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer-Verlag 01.05.2010 Springer Springer Nature B.V
Témata:	Applied sciences Calculus of variations and optimal control Calculus of Variations and Optimal Control; Optimization Combinatorics Exact sciences and technology Full Length Paper Localization Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operational research and scientific management Operational research. Management science Sciences and techniques of general use Studies Theorems Theoretical Generalized equations Variational analysis 49J53 49K40 Inverse function theorems Newton’s method Perturbations Implicit function theorems 65J15 Strong regularity Variational inequalities 90C3l Sensitivity analysis Modeling 90C31 Variational inequality Variational calculus Implicit function theorem Newton's method Newton method Regularity Mathematical programming
ISSN:	0025-5610, 1436-4646
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Popis
Shrnutí:	In an extension of Newton’s method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton’s iterates as elements of a sequence space. An inverse function version of this result shows that the strong regularity of the mapping associated with the Newton sequences is equivalent to the strong regularity of the generalized equation mapping.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0025-5610 1436-4646
DOI:	10.1007/s10107-009-0322-5