# Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics

arXiv: https://arxiv.org/abs/2103.12675 · HTML: https://mlsanity.com/paper/2103.12675/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [Accelerated First-Order Optimization under Nonlinear Constraints](https://mlsanity.com/paper/2302.00316/) (2023)
- [Accelerated forward-backward and Douglas-Rachford splitting dynamics](https://mlsanity.com/paper/2407.20620/) (2024)
- [Stability of Primal-Dual Gradient Flow Dynamics for Multi-Block Convex Optimization Problems](https://mlsanity.com/paper/2408.15969/) (2024)

## Abstract (arXiv)

In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are respectively associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.