Solving systems of linear equations by distributed convex optimization in the presence of stochastic uncertainty

Jing Wang, Nicola Elia

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

9 Scopus citations

Abstract

In this paper, we propose distributed optimization methods to solve systems of linear equations. We provide convergence analysis for both continuous and discrete time computation models based on linear systems theory. It is shown that the proposed computation approaches work for very general linear equations, scalable with data sets and can be implemented in distributed or parallel fashion. Furthermore, we show that the discrete time algorithm admits constant update step size in the presence of additive uncertainties. This robustness feature makes the approach computationally efficient and supplementary to the existing approaches to deal with uncertainties such as stochastic (sub-)gradient methods and sample averaging.

Original languageEnglish (US)
Title of host publication19th IFAC World Congress IFAC 2014, Proceedings
EditorsEdward Boje, Xiaohua Xia
PublisherIFAC Secretariat
Pages1210-1215
Number of pages6
ISBN (Electronic)9783902823625
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa
Duration: Aug 24 2014Aug 29 2014

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Volume19
ISSN (Print)1474-6670

Other

Other19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
CountrySouth Africa
CityCape Town
Period8/24/148/29/14

Keywords

  • Additive uncertainties
  • Distributed and parallel computation
  • Distributed optimization
  • Noises
  • Stochastic programming
  • Systems of linear equations

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  • Cite this

    Wang, J., & Elia, N. (2014). Solving systems of linear equations by distributed convex optimization in the presence of stochastic uncertainty. In E. Boje, & X. Xia (Eds.), 19th IFAC World Congress IFAC 2014, Proceedings (pp. 1210-1215). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 19). IFAC Secretariat. https://doi.org/10.3182/20140824-6-za-1003.02706