# Analysis of Newton-Raphson Consensus for multi-agent convex optimization under asynchronous and lossy communications

## TL;DR

This paper extends the Newton-Raphson consensus algorithm for multi-agent convex optimization to handle asynchronous, directed, and lossy communication networks, providing theoretical guarantees and empirical comparisons with subgradient methods.

## Contribution

It introduces a robust version of Newton-Raphson consensus that ensures local exponential convergence despite communication challenges, supported by theoretical analysis and simulations.

## Key findings

- Algorithm guarantees convergence under packet loss.
- Outperforms asynchronous subgradient methods in simulations.
- Provides conditions for stability and convergence.

## Abstract

We extend a multi-agent convex-optimization algorithm named Newton-Raphson consensus to a network scenario that involves directed, asynchronous and lossy communications. We theoretically analyze the stability and performance of the algorithm and, in particular, provide sufficient conditions that guarantee local exponential convergence of the node-states to the global centralized minimizer even in presence of packet losses. Finally, we complement the theoretical analysis with numerical simulations that compare the performance of the Newton-Raphson consensus against asynchronous implementations of distributed subgradient methods on real datasets extracted from open-source databases.