# Asymptotic for a second order evolution equation with convex potential and vanishing damping term

arXiv: https://arxiv.org/abs/1509.05598 · HTML: https://mlsanity.com/paper/1509.05598/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2015.

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

- [Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization](https://mlsanity.com/paper/2311.10053/) (2023)

## Abstract (arXiv)

In this short note, we recover by a different method the new result due to Attouch, Peyrouqet and Redont concerning the weak convergence as trightarrow+∞ of solutions x(t) to the second order differential equation [ xprimeprime(t)+fracKtxprime(t)+nablaPhi(x(t))=0, ] where K>3 and Phi is a smooth convex function defined on an Hilbert Space H. Moreover, we improve slightly their result on the rate of convergence of Phi(x(t))-minPhi.