Distributed Optimization With Local Domains: Applications in MPC and Network Flows

TL;DR

This paper introduces a communication-efficient distributed optimization algorithm for networks with local domain constraints, improving convergence speed and reducing communication costs in applications like MPC and network flows.

Contribution

The paper presents a novel distributed algorithm that leverages intersecting local domains to enhance communication efficiency in network optimization tasks.

Findings

Requires less communication to converge than prior algorithms

Effective in large network experiments

Applicable to MPC and network flow problems

Abstract

In this paper we consider a network with $P$ nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^\star$ minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function depends only on some components of the variable. Consequently, each node is interested in knowing only some components of $x^\star$, not the entire vector. This allows for improvement in communication-efficiency. We apply our algorithm to model predictive control (MPC) and to network flow problems and show, through experiments on large networks, that our proposed algorithm requires less communications to converge than prior algorithms.