Consensus-Based Distributed Optimization for Multiagent Systems Over Multiplex Networks

Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks consisting of multiple interacting networks. However, despite significant research on distributed optimization for single-layer networks, similar progress is lacking for multilayer systems. This article proposes two algorithms for distributed optimization problems in multiplex networks using the supra-Laplacian matrix and its diffusion dynamics. The algorithms include a distributed saddle-point algorithm and its variation as a distributed gradient descent algorithm. By relating consensus and diffusion dynamics, we obtain the multiplex supra-Laplacian matrix. We extend the distributed gradient descent algorithm for multiplex networks using this matrix and analyze the convergence of both algorithms with several theoretical results. Numerical examples validate our proposed algorithms, and we explore the impact of interlayer diffusion on consensus time. We also present a coordinated dispatch for interdependent infrastructure networks (energy–gas) to demonstrate the application of the proposed framework to real engineering problems.