# On Weakly Contracting Dynamics for Convex Optimization

arXiv: https://arxiv.org/abs/2403.07572 · HTML: https://mlsanity.com/paper/2403.07572/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2024.

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

- [Predictive Coding with Bayesian Priors via Proximal Gradients](https://mlsanity.com/paper/2606.08374/) (2026)

## Abstract (arXiv)

We analyze the convergence behavior of globally weakly and locally strongly contracting dynamics. Such dynamics naturally arise in the context of convex optimization problems with a unique minimizer. We show that convergence to the equilibrium is linear-exponential, in the sense that the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. As we show, the linear-exponential dependency arises naturally in certain dynamics with saturations. Additionally, we provide a sufficient condition for local input-to-state stability. Finally, we illustrate our results on, and propose a conjecture for, continuous-time dynamical systems solving linear programs.