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Dual decomposition has been successfully employed in a variety of distributedconvex optimization problems solved by a network of computing and communicatingnodes. Often, when the cost function is separable but the constraints arecoupled, the dual decomposition scheme involves local parallel subgradientcalculations and a global subgradient update performed by a master node. Inthis paper, we propose a consensus-based dual decomposition to remove the needfor such a master node and still enable the computing nodes to generate anapproximate dual solution for the underlying convex optimization problem. Inaddition, we provide a primal recovery mechanism to allow the nodes to haveaccess to approximate near-optimal primal solutions. Our scheme is based on aconstant stepsize choice and the dual and primal objective convergence areachieved up to a bounded error floor dependent on the stepsize and on thenumber of consensus steps among the nodes.

Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization