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...

Full description

Saved in:
Bibliographic Details
Published in:Automatica (Oxford) Vol. 129; p. 109608
Main Authors: Moradian, Hossein, Kia, Solmaz S.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.07.2021
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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