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arXiv · 2403.16165

Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization

Torbjørn Cunis·Ilya Kolmanovsky
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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.

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Torbjørn Cunis, Ilya Kolmanovsky. 2024-03-24. Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization. https://doi.org/10.1109/cdc56724.2024.10885904

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