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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Vydané v:	Automatica (Oxford) Ročník 129; s. 109608
Hlavní autori:	Moradian, Hossein, Kia, Solmaz S.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.07.2021
Predmet:	Augmented Lagrangian Distributed constrained convex optimization Optimal resource allocation Penalty function methods Primal–dual solutions Distributed constrained convex optimization Optimal resource allocation Penalty function methods Augmented Lagrangian Primal–dual solutions
ISSN:	0005-1098, 1873-2836
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Popis
Shrnutí:	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.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/j.automatica.2021.109608