%0 Conference Paper %1 10885904 %A Cunis, Torbjørn %A Kolmanovsky, Ilya %B 2024 IEEE 63rd Conference on Decision and Control (CDC) %D 2024 %K myown %P 5950-5956 %R 10.1109/CDC56724.2024.10885904 %T Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization⋆ %X We show that Newton methods for generalized equations are input-to-state stable with respect to perturbations such as due to inexact computations. We then use this result to obtain convergence and robustness of a multistep Newton-type method for multivariate generalized equations. We demonstrate the usefulness of the results with other applications to nonlinear optimization. In particular, we provide a new proof for (robust) local convergence of the augmented Lagrangian method.

@inproceedings{10885904, abstract = {We show that Newton methods for generalized equations are input-to-state stable with respect to perturbations such as due to inexact computations. We then use this result to obtain convergence and robustness of a multistep Newton-type method for multivariate generalized equations. We demonstrate the usefulness of the results with other applications to nonlinear optimization. In particular, we provide a new proof for (robust) local convergence of the augmented Lagrangian method.}, added-at = {2025-04-15T22:53:50.000+0200}, author = {Cunis, Torbjørn and Kolmanovsky, Ilya}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2fce9fc6185e47152f023f90ce8455459/tcunis}, booktitle = {2024 IEEE 63rd Conference on Decision and Control (CDC)}, doi = {10.1109/CDC56724.2024.10885904}, interhash = {fb8eec0cc648745357bc520a19a27958}, intrahash = {fce9fc6185e47152f023f90ce8455459}, issn = {2576-2370}, keywords = {myown}, pages = {5950-5956}, timestamp = {2025-04-15T23:18:10.000+0200}, title = {Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization⋆}, year = 2024 }