Two-Facet Scalable Cooperative Optimization of Multi-Agent Systems in the Networked Environment

Cooperatively optimizing a vast number of agents over a large-scale network faces unprecedented scalability challenges. The scalability of existing optimization algorithms is limited by either the agent population size or the network dimension. As a radical improvement, this article, for the first time, constructs a two-facet scalable distributed optimization framework. This novel framework distributes the computing load among agents (scalability w.r.t. population size) and enables each agent to only consider partial network constraints in its primal variable updates (scalability w.r.t. network dimension). We first develop a systemic network dimension reduction technique to virtually cluster the agents and lower the dimension of network-induced constraints and then constitute a novel shrunken primal-multi-dual subgradient (SPMDS) algorithm based on the reduced-dimension network for strongly coupled convex optimization problems. Optimality and convergence of the proposed distributed optimization framework are rigorously proved. The SPMDS-based optimization framework is free of agent-to-agent or cluster-to-cluster communication. Besides, the proposed method can achieve significant floating-point operations (FLOPs) reduction compared with full-dimension cases. The efficiency and efficacy of the proposed approaches are demonstrated, in comparison with benchmark methods, through simulations of electric vehicle charging control problems and traffic congestion control problems.