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

Published 24 Mar 2024 in math.OC, cs.SY, and eess.SY | (2403.16165v2)

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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