Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 7; no. 1; pp. 483 - 492
Main Authors: Notarnicola, Ivano, Notarstefano, Giuseppe
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Constraint-coupled optimization
Control systems
Convergence
Cost function
Couplings
Distributed algorithms
Distributed generation
distributed optimization
microgrid control
Network control
Nickel
Optimization
Predictive control
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the latter involving all the decision variables. We propose a novel fully distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation, based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node finds a primal-dual optimal solution pair of a local relaxed version of the original problem and then updates suitable auxiliary local variables. We prove that agents asymptotically compute their portion of an optimal (feasible) solution of the original problem. This primal recovery property is obtained without any averaging mechanism typically used in dual decomposition methods. To corroborate the theoretical results, we show how the methodology applies to an instance of a distributed model-predictive control scheme in a microgrid control scenario.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2019.2925267