Journal
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
Volume 7, Issue 1, Pages 483-492Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCNS.2019.2925267
Keywords
Constraint-coupled optimization; distributed optimization; microgrid control
Funding
- European Research Council under the European Union's Horizon 2020 Research and Innovation Program [638992-OPT4SMART]
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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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