# Passivity-Based Distributed Optimization with Communication Delays Using PI Consensus Algorithm

arXiv: https://arxiv.org/abs/1609.04666 · HTML: https://mlsanity.com/paper/1609.04666/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2016.

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

- [Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methods](https://mlsanity.com/paper/2202.06922/) (2022)
- [A primal-dual perspective for distributed TD-learning](https://mlsanity.com/paper/2310.00638/) (2023)
- [On Linear Convergence of PI Consensus Algorithm under the Restricted Secant Inequality](https://mlsanity.com/paper/2310.00419/) (2023)

## Abstract (arXiv)

In this paper, we address a class of distributed optimization problems in the presence of inter-agent communication delays based on passivity. We first focus on unconstrained distributed optimization and provide a passivity-based perspective for distributed optimization algorithms. This perspective allows us to handle communication delays while using scattering transformation. Moreover, we extend the results to constrained distributed optimization, where it is shown that the problem is solved by just adding one more feedback loop of a passive system to the solution of the unconstrained ones. We also show that delays can be incorporated in the same way as the unconstrained problems. Finally, the algorithm is applied to a visual human localization problem using a pedestrian detection algorithm.