Continuous Newton-like Methods featuring Inertia and Variable Mass - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Continuous Newton-like Methods featuring Inertia and Variable Mass

Résumé

We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the acceleration, called variable mass. For strongly convex optimization, we provide guarantees on how the Newtonian and inertial behaviors of the system can be non-asymptotically controlled by means of this variable mass. A connection with the Levenberg-Marquardt (or regularized Newton's) method is also made. We then show the effect of the variable mass on the asymptotic rate of convergence of the dynamics, and in particular, how it can turn the latter into an accelerated Newton method. We provide numerical experiments supporting our findings. This work represents a significant step towards designing new algorithms that benefit from the best of both first- and second-order optimization methods.
Fichier principal
Vignette du fichier
2301.08726.pdf (1.02 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03951620 , version 1 (23-01-2023)

Licence

Identifiants

  • HAL Id : hal-03951620 , version 1

Citer

Camille Castera, Hedy Attouch, Jalal Fadili, Peter Ochs. Continuous Newton-like Methods featuring Inertia and Variable Mass. 2023. ⟨hal-03951620⟩
34 Consultations
35 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More