Lyapunov analysis of a distributed optimization scheme

We analyze the convergence of the distributed multi-agent optimization scheme originally proposed in [1]. In this scheme, a number of agents cooperate to estimate the minimum of the sum of their locally-known cost functions. We consider a special case for which the collective cost function is strongly convex and where the agent communication graph is fixed. Whereas the analysis in [1] focuses on the suboptimality of the Cesàro averages of the agents´ sequences, we establish explicit ultimate bounds on the agents´ estimation errors themselves. We demonstrate that the collective optimum is globally practically asymptotically stable for this algorithm.