Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

TL;DR

This paper introduces a continuous-time proportional-integral method for distributed optimization in networked systems, unifying dual decomposition and consensus approaches with proven convergence.

Contribution

It develops a novel continuous-time proportional-integral algorithm for distributed optimization, bridging dual decomposition and consensus methods with stability guarantees.

Findings

Unified framework for dual decomposition and consensus methods

Proposed continuous-time PI algorithm with convergence proof

Applicable to multi-agent networked systems

Abstract

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.