Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization
Optimization and Control
2025-03-18 v2 Systems and Control
Systems and Control
Abstract
We show that Newton methods for generalized equations are input-to-state stable with respect to disturbances 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.
Cite
@article{arxiv.2403.16165,
title = {Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization},
author = {Torbjørn Cunis and Ilya Kolmanovsky},
journal= {arXiv preprint arXiv:2403.16165},
year = {2025}
}
Comments
Submitted to 2024 Conference on Decision and Control