Lyapunov Analysis of a Distributed Optimization Scheme

Karla Kvaternik (1) , Lacra Pavel (1)

1 ECE - Department of Electrical and Computer Engineering [University of Toronto]

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 Ces'aro 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.

Domains: Networking and Internet Architecture [cs.NI]

Karla Kvaternik, Lacra Pavel. Lyapunov Analysis of a Distributed Optimization Scheme. NetGCOOP 2011 : International conference on NETwork Games, COntrol and OPtimization, Telecom SudParis et Université Paris Descartes, Oct 2011, Paris, France. ⟨hal-00644455⟩