Distributed optimization in an energy-constrained network

Alireza Razavi, Zhi Quan Luo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We consider a distributed optimization probiert! whereby two nodes S 1, S2 wish to jointly minimize a common convex quadratic cost function, f(x1, x2), subject to separate local constraints on x1 and x2, respectively. Suppose that node S1 has control of variable x1 only and node S2 has control of variable x2 only. The two nodes locally update their respective variables and periodically exchange their values over a noisy channel. Previous studies of this problem have mainly focused on the convergence issue and the analysis of convergence, rate. In this work, we focus on the communication energy and study its impact on convergence, In particular, we consider a class of distributed stochastic gradient type algorithms implemented using certain linear analog messaging schemes. We study the minimum amount of communication energy required for the two nodes to compute an ε-minimizer of f(x1, x2) in the mean square sense. Our analysis shows that the communication energy must grow at least at the rate of Ω(ε-1). We also derive specific designs which attain this minimum energy bound, and provide simulation results that confirm our theoretical analysis. Extension to the multiple node case is described.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
PagesIII189-III192
DOIs
StatePublished - 2007
Event2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 - Honolulu, HI, United States
Duration: Apr 15 2007Apr 20 2007

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
ISSN (Print)1520-6149

Other

Other2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
Country/TerritoryUnited States
CityHonolulu, HI
Period4/15/074/20/07

Keywords

  • Convergence
  • Distributed optimization
  • Energy constraint
  • Sensor networks
  • Stochastic gradient method

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