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

Jing Wang; Nicola Elia

doi:10.3182/20140824-6-za-1003.02706

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 proceeding › Conference contribution

14 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 language	English (US)
Title of host publication	19th IFAC World Congress IFAC 2014, Proceedings
Editors	Edward Boje, Xiaohua Xia
Publisher	IFAC Secretariat
Pages	1210-1215
Number of pages	6
ISBN (Electronic)	9783902823625
DOIs	https://doi.org/10.3182/20140824-6-za-1003.02706
State	Published - 2014
Externally published	Yes
Event	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa Duration: Aug 24 2014 → Aug 29 2014

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	19
ISSN (Print)	1474-6670

Other

Other	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
Country/Territory	South Africa
City	Cape Town
Period	8/24/14 → 8/29/14

Bibliographical note

Funding Information:
★ This research has been supported under NSF grant CNS-1239319. 1 We would like to thank Prof. P.G. Voulgaris and Prof. S. Salapaka for introducing us to the problem and the stimulating discussions on alternative approaches. 2 Our approach also works for more general rectangular matrices A. Here we assume A to be a square matrix since it is easy to elaborate our approach and represents an important class of problems.

Publisher Copyright:
© IFAC.

Keywords

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

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Solving systems of linear equations by distributed convex optimization in the presence of stochastic uncertainty. / Wang, Jing; Elia, Nicola.
19th IFAC World Congress IFAC 2014, Proceedings. ed. / Edward Boje; Xiaohua Xia. IFAC Secretariat, 2014. p. 1210-1215 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 19).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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. IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 19, IFAC Secretariat, pp. 1210-1215, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, Cape Town, South Africa, 8/24/14. https://doi.org/10.3182/20140824-6-za-1003.02706

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

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