An augmented Lagrangian method for distributed optimization

We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization prob...

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Bibliographic Details
Published in:Mathematical programming 2015-08, Vol.152 (1-2), p.405-434
Main Authors: Chatzipanagiotis, Nikolaos, Dentcheva, Darinka, Zavlanos, Michael M.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Convergence
Convex analysis
Decomposition
Full Length Paper
Lagrange multiplier
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Network management systems
Networks
Numerical Analysis
Optimization
Stochasticity
Studies
Theoretical
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Summary:We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization problem. The proposed method compares favorably to two augmented Lagrangian decomposition methods known in the literature, as well as to decomposition methods based on the ordinary Lagrangian function.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0808-7