# Tikhonov regularization of a second order dynamical system with Hessian driven damping

arXiv: https://arxiv.org/abs/1911.12845 · HTML: https://mlsanity.com/paper/1911.12845/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Inertial Newton Algorithms Avoiding Strict Saddle Points](https://mlsanity.com/paper/2111.04596/) (2021)

## Abstract (arXiv)

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.