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

Andrea Simonetto () and Hadi Jamali-Rad ()
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Andrea Simonetto: Delft University of Technology
Hadi Jamali-Rad: Delft University of Technology

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 1, No 9, 172-197

Abstract: 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.

Keywords: Distributed convex optimization; Dual decomposition; Primal recovery; Consensus algorithm; Subgradient optimization; Epsilon-subgradient; Ergodic convergence; 90C25; 90C30; 90C46; 90C59 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-015-0758-0

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