Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
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 subgr...
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| Veröffentlicht in: | Journal of optimization theory and applications 2016-01, Vol.168 (1), p.172-197 |
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| container_title | Journal of optimization theory and applications |
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| creator | Simonetto, Andrea Jamali-Rad, Hadi |
| description | 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. |
| doi_str_mv | 10.1007/s10957-015-0758-0 |
| format | Article |
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| subjects | Algorithms Applications of Mathematics Approximation Calculus of Variations and Optimal Control Optimization Computation Computational geometry Convergence Convex analysis Convexity Decomposition Engineering Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Recovery Studies Theory of Computation |
| title | Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization |
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