Cluster-based distributed augmented Lagrangian algorithm for a class of constrained convex optimization problems
We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimizati...
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| Vydáno v: | Automatica (Oxford) Ročník 129; s. 109608 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.07.2021
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimization problem is the sum of the local convex costs of the subagents of each cluster. We seek a minimizer of this cost subject to a set of affine equality constraints, and a set of affine inequality constraints specifying the bounds on the decision variables if such bounds exist. We design our distributed algorithm in a cluster-based framework which results in a significant reduction in communication and computation costs. Our proposed distributed solution is a novel continuous-time algorithm that is linked to the augmented Lagrangian approach. It converges asymptotically when the local cost functions are convex and exponentially when they are strongly convex and have Lipschitz gradients. Moreover, we use an ϵ-exact penalty function to address the inequality constraints and derive an explicit lower bound on the penalty function weight to guarantee convergence to ϵ-neighborhood of the global minimum value of the cost. A numerical example demonstrates our results. |
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| AbstractList | We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimization problem is the sum of the local convex costs of the subagents of each cluster. We seek a minimizer of this cost subject to a set of affine equality constraints, and a set of affine inequality constraints specifying the bounds on the decision variables if such bounds exist. We design our distributed algorithm in a cluster-based framework which results in a significant reduction in communication and computation costs. Our proposed distributed solution is a novel continuous-time algorithm that is linked to the augmented Lagrangian approach. It converges asymptotically when the local cost functions are convex and exponentially when they are strongly convex and have Lipschitz gradients. Moreover, we use an ϵ-exact penalty function to address the inequality constraints and derive an explicit lower bound on the penalty function weight to guarantee convergence to ϵ-neighborhood of the global minimum value of the cost. A numerical example demonstrates our results. |
| ArticleNumber | 109608 |
| Author | Kia, Solmaz S. Moradian, Hossein |
| Author_xml | – sequence: 1 givenname: Hossein surname: Moradian fullname: Moradian, Hossein email: hmoradia@uci.edu – sequence: 2 givenname: Solmaz S. surname: Kia fullname: Kia, Solmaz S. email: solmaz@uci.edu |
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| Cites_doi | 10.1016/j.automatica.2016.07.003 10.1561/2200000016 10.1109/TNET.2013.2251896 10.1109/TWC.2006.1687734 10.1016/0167-6377(85)90030-6 10.1109/TAC.2015.2449811 10.1016/j.sysconle.2018.10.007 10.1109/TCOMM.2004.831346 10.1016/j.ifacol.2018.12.040 10.1109/TPWRS.2012.2188912 10.1109/TAC.2013.2275667 10.1109/TAC.2014.2363299 10.1109/PESGM.2012.6345156 10.1109/CDC.2011.6160931 10.1109/TAC.2011.2161027 10.23919/ACC.2017.7963458 10.1109/CDC.2018.8619343 10.1016/j.automatica.2015.03.001 10.1016/j.ifacol.2016.05.003 10.1109/CDC.2011.6161503 10.1109/TCNS.2015.2399191 10.1007/BFb0120696 10.1109/CDC.2018.8619760 10.1016/j.sysconle.2017.07.012 10.23919/ACC.2018.8431779 10.1109/CDC.2017.8264654 10.1109/CDC.2018.8619651 10.1016/j.orl.2012.11.009 10.1007/s10957-006-9080-1 10.1016/j.automatica.2016.08.007 10.1109/TSP.2011.2169407 10.1109/CDC.2018.8619512 10.1109/TSG.2017.2684183 10.1109/CDC.2012.6426665 |
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| Keywords | Distributed constrained convex optimization Optimal resource allocation Penalty function methods Augmented Lagrangian Primal–dual solutions |
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| SubjectTerms | Augmented Lagrangian Distributed constrained convex optimization Optimal resource allocation Penalty function methods Primal–dual solutions |
| Title | Cluster-based distributed augmented Lagrangian algorithm for a class of constrained convex optimization problems |
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