# Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

arXiv: https://arxiv.org/abs/1309.6613 · HTML: https://mlsanity.com/paper/1309.6613/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2013.

## Built on by (most cited first, 2 of 2)

- [Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective](https://mlsanity.com/paper/2204.12663/) (2022)
- [Distributed Unconstrained Optimization with Time-varying Cost Functions](https://mlsanity.com/paper/2212.09472/) (2022)

## Abstract (arXiv)

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.