Distributed optimization in an energy-constrained network: Analog versus digital communication schemes

Alireza Razavi, Wenbo Zhang, Zhi Quan Luo

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider a distributed optimization problem whereby a network of n nodes, Sℓell; 1 n, wishes to minimize a common strongly convex function f(x), x=[1 xn]T, under the constraint that node S controls variable x only. The nodes locally update their respective variables and periodically exchange their values with their neighbors over a set of predefined communication channels. Previous studies of this problem have focused mainly on the convergence issue and the analysis of convergence rate. In this study, we consider noisy communication channels and study the impact of communication energy on convergence. In particular, we study the minimum amount of communication energy required for nodes to obtain an \epsilon-minimizer of f(x) in the mean square sense. For linear analog communication schemes, we prove that the communication energy to obtain an epsilon-minimizer of f(x) must grow at least at the rate of Ω (1ε), and this bound is tight when f is convex quadratic. Furthermore, we show that the same energy requirement can be reduced to O(21ε ) if a suitable digital communication scheme is used.

Original languageEnglish (US)
Article number6238359
Pages (from-to)1803-1817
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 2013


  • Communication energy
  • distributed optimization
  • energy-constrained network


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