Distributed average consensus with least-mean-square deviation

Lin Xiao, Stephen Boyd, Seung Jean Kim

Research output: Contribution to journalArticlepeer-review

821 Scopus citations


We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted average of its neighbors' values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total mean-square deviation of the individual variables from their average, which converges to a steady-state value. We consider the problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state. We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. We describe some computational methods for solving this problem, and compare the weights and the mean-square deviations obtained by this method and several other weight design methods.

Original languageEnglish
Pages (from-to)33-46
Number of pages14
JournalJournal of Parallel and Distributed Computing
Issue number1
StatePublished - Jan 2007
Externally publishedYes


  • Convex optimization
  • Distributed average consensus
  • Edge-transitive graphs
  • Least-mean-square


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