Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 60, Issue 4, Pages 922-936Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2014.2363299
Keywords
Augmented Lagrangian; consensus; convergence rate; distributed optimization
Funding
- Carnegie Mellon\Portugal Program under Fundacao de Ciencia e Tecnologia (FCT) from Portugal
- FCT [CMU-PT/SIA/0026/2009, FCT PTDC/EMS-CRO/2042/2012, SFRH/BD/33518/2008]
- ISR/IST
- AFOSR [FA95501010291]
- NSF [CCF1011903]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1011903] Funding Source: National Science Foundation
- Fundação para a Ciência e a Tecnologia [SFRH/BD/33518/2008] Funding Source: FCT
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We study distributed optimization where nodes cooperatively minimize the sum of their individual, locally known, convex costs f(i)(x)'s; x is an element of R-d is global. Distributed augmented Lagrangian (AL) methods have good empirical performance on several signal processing and learning applications, but there is limited understanding of their convergence rates and how it depends on the underlying network. This paper establishes globally linear (geometric) convergence rates of a class of deterministic and randomized distributed AL methods, when the f(i)'s are twice continuously differentiable and have a bounded Hessian. We give explicit dependence of the convergence rates on the underlying network parameters. Simulations illustrate our analytical findings.
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