Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization
<|reference_start|>Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization: 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.<|reference_end|>
@article{cunis2024input-to-state,
    title={Input-to-State Stability of Newton Methods for Generalized Equations in
  Nonlinear Optimization},
    author={Torbj{o}rn Cunis and Ilya Kolmanovsky},
    journal={arXiv preprint arXiv:2403.16165},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16165},
    primaryClass={math.OC cs.SY eess.SY}
}