A Duality-Based Approach for Distributed Optimization with Coupling Constraints

TL;DR

This paper introduces a novel distributed optimization algorithm leveraging duality theory to efficiently solve convex problems with coupling constraints, ensuring correctness and demonstrating effectiveness through numerical experiments.

Contribution

It presents a new distributed algorithm based on primal relaxation and duality, with a simple structure and proven correctness for problems with coupling constraints.

Findings

Algorithm is correct and converges as shown theoretically.

Numerical results demonstrate effectiveness and practicality.

Approach simplifies complex duality-based derivations.

Abstract

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node solves a local version of the original problem relaxation, and updates suitable dual variables. We prove the algorithm correctness and show its effectiveness via numerical computations.