# Tracking-ADMM for Distributed Constraint-Coupled Optimization

arXiv: https://arxiv.org/abs/1907.10860 · HTML: https://mlsanity.com/paper/1907.10860/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Decentralized gradient descent maximization method for composite nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2304.02441/) (2023)
- [Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics](https://mlsanity.com/paper/2203.14527/) (2022)
- [Decentralized and Equitable Optimal Transport](https://mlsanity.com/paper/2403.04259/) (2024)
- [Estimation Network Design framework for efficient distributed optimization](https://mlsanity.com/paper/2404.15273/) (2024)
- [Decentralized Optimization with Cross-Coupled Mixed Affine Constraints](https://mlsanity.com/paper/2609.33021/) (2026)

## Abstract (arXiv)

We consider constraint-coupled optimization problems in which agents of a network aim to cooperatively minimize the sum of local objective functions subject to individual constraints and a common linear coupling constraint. We propose a novel optimization algorithm that embeds a dynamic average consensus protocol in the parallel Alternating Direction Method of Multipliers (ADMM) to design a fully distributed scheme for the considered set-up. The dynamic average mechanism allows agents to track the time-varying coupling constraint violation (at the current solution estimates). The tracked version of the constraint violation is then used to update local dual variables in a consensus-based scheme mimicking a parallel ADMM step. Under convexity, we prove that all limit points of the agents' primal solution estimates form an optimal solution of the constraint-coupled (primal) problem. The result is proved by means of a Lyapunov-based analysis simultaneously showing consensus of the dual estimates to a dual optimal solution, convergence of the tracking scheme and asymptotic optimality of primal iterates. A numerical study on optimal charging schedule of plug-in electric vehicles corroborates the theoretical results.