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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Bibliographic Details
Published in:Mathematical programming Vol. 123; no. 1; pp. 139 - 159
Main Authors: Dontchev, A. L., Rockafellar, R. T.
Format: Journal Article Conference Proceeding
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.05.2010
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-009-0322-5