A dual ascent algorithm for asynchronous distributed optimization with unreliable directed communications

TL;DR

This paper presents a dual ascent algorithm for asynchronous distributed optimization over unreliable directed networks, extending consensus algorithms with a new optimization perspective and demonstrating its effectiveness through simulations.

Contribution

It introduces a dual ascent approach for distributed optimization on unreliable directed graphs, linking consensus algorithms to optimization theory.

Findings

The algorithm converges under unreliable directed communications.

Numerical simulations show effectiveness for smooth and nonsmooth functions.

The dual interpretation enhances understanding of consensus-based optimization.

Abstract

We show that the averaged consensus algorithm on directed graphs with unreliable communications by Bof-Carli-Schenato has a dual optimization interpretation, which could be extended to the case of distributed optimization. We report on our numerical simulations for the distributed optimization algorithm for smooth and nonsmooth functions.