Abstract
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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This work was supported by National Science Foundation.
A. L. Dontchev is on leave from Mathematical Reviews, AMS, Ann Arbor, MI, and from the Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria.
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Dontchev, A.L., Rockafellar, R.T. Newton’s method for generalized equations: a sequential implicit function theorem. Math. Program. 123, 139–159 (2010). https://doi.org/10.1007/s10107-009-0322-5
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DOI: https://doi.org/10.1007/s10107-009-0322-5
Keywords
- Newton’s method
- Generalized equations
- Variational inequalities
- Strong regularity
- Implicit function theorems
- Inverse function theorems
- Perturbations
- Variational analysis