Distributed optimization in an energy-constrained network using a digital communication scheme

Alireza Razavi, Zhi Quan Luo

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

Abstract

We consider a distributed optimization problem where n nodes, S l, l ∈ {1, . . . , n}, wish to minimize a common strongly convex function f(x), x = [x1, . . . , xn]T , and suppose that node Sl only has control of variable xl. The nodes locally update their respective variables and periodically exchange their values over noisy channels. 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 study the minimum amount of communication energy required for nodes to obtain an ∈-minimizer of f(x) in the mean square sense. In an earlier work, we considered analog communication schemes and proved that the communication energy must grow at the rate of Ω (∈-1) to obtain an ∈-minimizer of a convex quadratic function. In this paper, we consider digital communication schemes and propose a distributed algorithm which only requires communication energy of O((log ∈-1)3) to obtain an ∈-minimizer of f(x). Furthermore, the algorithm provided herein converges linearly. Thus, distributed optimization with digital communication schemes is significantly more energy efficient than with analog communication schemes.

Original languageEnglish (US)
Title of host publication2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
Pages2401-2404
Number of pages4
DOIs
StatePublished - Sep 23 2009
Event2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009 - Taipei, Taiwan, Province of China
Duration: Apr 19 2009Apr 24 2009

Publication series

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

Other

Other2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
CountryTaiwan, Province of China
CityTaipei
Period4/19/094/24/09

Keywords

  • Convergence
  • Distributed optimization
  • Energy constraint
  • Sensor networks

Fingerprint Dive into the research topics of 'Distributed optimization in an energy-constrained network using a digital communication scheme'. Together they form a unique fingerprint.

Cite this