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

Cooperatively optimizing a vast number of agents that are connected over a large-scale network brings unprecedented scalability challenges. This paper revolves around problems optimizing coupled objective functions under coupled network-induced constraints and local constraints. The scalability of existing optimization paradigms is limited by either the agent population size or the network dimension. As a radical improvement, this paper for the first time constructs a two-facet scalable decentralized optimization framework. To this end, we first develop a systemic network dimension reduction technique to virtually cluster the agents and lower the dimension of network-induced constraints, then constitute a novel shrunken-primal-multi-dual subgradient (SPMDS) algorithm based on the reduced-dimension network. Rigorous optimality and convergence analyses of the proposed decentralized optimization framework are provided. The SPMDS-based optimization framework is free of agent-to-agent communication and no additional aggregators are required for agent clusters. 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.