An adaptive dynamic protocol for distributed convex optimization

This article considers the distributed convex optimization problem over a linear multi-agent system using an adaptive dynamic protocol. The communication network topology among the agents are assumed to be undirected and fixed. The global cost function of the network is strictly convex and is given by the sum of the local cost functions associated to each agents. It is proved that under the proposed protocol, the agents can reach an agreement on a common state value which optimizes the global cost function.