A fully distributed dual gradient method with linear convergence for large-scale separable convex problems

Ion Necoara, Angelia Nedich

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

2 Citations (Scopus)

Abstract

In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we show that under the assumption that the Hessian of the primal objective function is bounded we have a global error bound type property for the dual problem. Using this error bound property we devise a fully distributed dual gradient scheme for which we derive global linear rate of convergence. The proposed dual gradient method is fully distributed, requiring only local information, since is based on a weighted stepsize. Our method can be applied in many applications, e.g. distributed model predictive control, network utility maximization or optimal power flow.

Original languageEnglish (US)
Title of host publication2015 European Control Conference, ECC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages304-309
Number of pages6
ISBN (Electronic)9783952426937
DOIs
StatePublished - Nov 16 2015
Externally publishedYes
EventEuropean Control Conference, ECC 2015 - Linz, Austria
Duration: Jul 15 2015Jul 17 2015

Other

OtherEuropean Control Conference, ECC 2015
CountryAustria
CityLinz
Period7/15/157/17/15

Fingerprint

Gradient methods
Model predictive control

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Necoara, I., & Nedich, A. (2015). A fully distributed dual gradient method with linear convergence for large-scale separable convex problems. In 2015 European Control Conference, ECC 2015 (pp. 304-309). [7330561] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECC.2015.7330561

A fully distributed dual gradient method with linear convergence for large-scale separable convex problems. / Necoara, Ion; Nedich, Angelia.

2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 304-309 7330561.

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

Necoara, I & Nedich, A 2015, A fully distributed dual gradient method with linear convergence for large-scale separable convex problems. in 2015 European Control Conference, ECC 2015., 7330561, Institute of Electrical and Electronics Engineers Inc., pp. 304-309, European Control Conference, ECC 2015, Linz, Austria, 7/15/15. https://doi.org/10.1109/ECC.2015.7330561
Necoara I, Nedich A. A fully distributed dual gradient method with linear convergence for large-scale separable convex problems. In 2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 304-309. 7330561 https://doi.org/10.1109/ECC.2015.7330561
Necoara, Ion ; Nedich, Angelia. / A fully distributed dual gradient method with linear convergence for large-scale separable convex problems. 2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 304-309
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