Approximations and generalized Newton methods

Abstract

We present approaches to (generalized) Newton methods in the framework of generalized equations $0\in f(x)+M(x)$, where $f$ is a function and $M$ is a multifunction. The Newton steps are defined by approximations $\hat f$ of $f$ and the solutions of $0\in \hat{f}(x)+M(x)$. We give a unified view of the local convergence analysis of such methods by connecting a certain type of approximation with the desired kind of convergence and different regularity conditions for $f+M$ Show more