Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912275523174400 |
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| author | Cunis, Torbjørn Kolmanovsky, Ilya |
| author_facet | Cunis, Torbjørn Kolmanovsky, Ilya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization Cunis, Torbjørn Kolmanovsky, Ilya Optimization and Control Systems and Control 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. |
| title | Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2403.16165 |