Stability of a regularized Newton method with two potentials

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.