On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems

In this paper we propose a fully distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and Lipschitz continuity of the gradient of the primal objecti...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 55; pp. 209 - 216
Main Authors: Necoara, Ion, Nedelcu, Valentin
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.05.2015
Subjects:
Distributed gradient algorithm
Dual decomposition
Error bound
Linear convergence
Separable convex problems
Dual decomposition
Separable convex problems
Error bound
Linear convergence
Distributed gradient algorithm
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:In this paper we propose a fully distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and Lipschitz continuity of the gradient of the primal objective function 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, i.e. a gradient scheme based on a weighted step size, for which we derive global linear rate of convergence for both dual and primal suboptimality and for primal feasibility violation. Numerical simulations are also provided to confirm our theory.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2015.02.038