Boushra Abbas

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 … Read more

Let $\Phi:\mathcal{H}\longrightarrow\mathbb{R\cup}\left\{ +\infty\right\} $ be a closed convex proper function on a real Hilbert space $\mathcal{H}$, and $\partial\Phi:\mathcal{H}\rightrightarrows\mathcal{H}$ its subdifferential. For any control function $\epsilon:\mathbb{R}_{+}\longrightarrow\mathbb{R}_{+}$ which tends to zero as $t$ goes to $+\infty$, and $\lambda$ a positive parameter, we study the asymptotic behavior of the trajectories of the regularized Newton dynamical system \begin{eqnarray*} & … Read more