Fast distributed optimization and game-theoretic methods in networked systems

This work provides an overview of the methods that solve distributed and game-theoretic optimization problems in multi-agent systems. All considered methods are based on the assumption that each agent has access only to some local information but not to the whole information in the system. However, each agent can communicate its local information with neighbors to achieve a common goal. The neighborhoods are defined through a communication graph. The focus is therefore on communication-based processes that possess rapid convergence to a system's optimum. The individual cost functions of the agents are assumed to be strictly convex with Lipschitz continuous gradients. Some fast methods for distributed optimization have been already presented in the literature. However, there are many open questions related to game-theoretic optimization. This work aims to provide a structured comparison between the known results for these two types of optimization problems and formulate potential directions for the future research.