# A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate

arXiv: https://arxiv.org/abs/2109.13467 · HTML: https://mlsanity.com/paper/2109.13467/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2021.

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

- [Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control](https://mlsanity.com/paper/2406.11168/) (2024)

## Abstract (arXiv)

This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential decay of a tailored Lyapunov function is established. Then several time discretizations of the continuous model are considered and analyzed via a unified discrete Lyapunov function. Moreover, two families of accelerated proximal alternating direction methods of multipliers are obtained, and nonergodic optimal mixed-type convergence rates shall be proved for the primal objective residual, the feasibility violation and the Lagrangian gap. Finally, numerical experiments are provided to validate the practical performances.