Stability of a regularized Newton method with two potentials

TL;DR

This paper investigates the stability of a regularized Newton method with two potentials in Hilbert spaces, focusing on its robustness and implications for numerical algorithms involving structured monotone operators.

Contribution

It introduces a stability analysis for a regularized Newton method with two potentials, allowing the regularization coefficient to vary and linking to combined forward-backward and Newton algorithms.

Findings

Stability results for the regularized Newton method are established.

The regularization coefficient can be of bounded variation.

Implications for numerical algorithms combining forward-backward and Newton methods.

Abstract

In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt regularization term acts in an open loop way. As a byproduct of our study, we can take the regularization coefficient of bounded variation. These stability results are directly related to the study of numerical algorithms that combine forward-backward and Newton's methods.