Abstract
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel subgradient calculations and a global subgradient update performed by a master node. In this paper, we propose a consensus-based dual decomposition to remove the need for such a master node and still enable the computing nodes to generate an approximate dual solution for the underlying convex optimization problem. In addition, we provide a primal recovery mechanism to allow the nodes to have access to approximate near-optimal primal solutions. Our scheme is based on a constant stepsize choice, and the dual and primal objective convergence are achieved up to a bounded error floor dependent on the stepsize and on the number of consensus steps among the nodes.
Original language | English |
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Pages (from-to) | 172-197 |
Number of pages | 26 |
Journal | Journal of Optimization Theory and Applications |
Volume | 168 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 |
Bibliographical note
HarvestFirst online 29-5-2015