Passivity-Based Local Design Conditions for Global Optimality in Distributed Convex Optimization

In recent times, various distributed optimization algorithms have been proposed for which global optimality and convergence are proven provided that all agents follow the specific algorithm. In this paper, we leverage passivity theory to first establish a distributed optimization framework with local design requirements for the agent dynamics in both unconstrained and constrained problems with undirected communication topologies. Under the roof of these requirements, the agents may use heterogeneous optimization algorithms without compromising global optimality and convergence. Subsequently, we propose some exemplary agent systems that comply with the established requirements. Compared to existing approaches, our algorithms do not require any global initialization nor communication of multiple variables. Consequently, the agents may leave or rejoin the networked optimization without compromising convergence to the correct global optimizer. Furthermore, we show that for unconstrained optimization, an extension to directed communication topologies is possible. Simulation results illustrate the plug-and-play capabilities and interoperability of the proposed agent dynamics.