2019/08/19 by Hossein Moradian, Moradian, Hossein, Solmaz S. Kia +1
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Mathematics #Multiagent Systems (cs.MA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1908.06634
openalex publication_date 2019/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a distributed solution for a constrained convex optimization\nproblem over a network of clustered agents each consisted of a set of\nsubagents. The communication range of the clustered agents is such that they\ncan form a connected undirected graph topology. The total cost in this\noptimization problem is the sum of the local convex costs of the subagents of\neach cluster. We seek a minimizer of this cost subject to a set of affine\nequality constraints, and a set of affine inequality constraints specifying the\nbounds on the decision variables if such bounds exist. We design our\ndistributed algorithm in a cluster-based framework which results in a\nsignificant reduction in communication and computation costs. Our proposed\ndistributed solution is a novel continuous-time algorithm that is linked to the\naugmented Lagrangian approach. It converges asymptotically when the local cost\nfunctions are convex and exponentially when they are strongly convex and have\nLipschitz gradients. Moreover, we use an \ε-exact penalty function to\naddress the inequality constraints and derive an explicit lower bound on the\npenalty function weight to guarantee convergence to \ε-neighborhood of\nthe global minimum value of the cost. A numerical example demonstrates our\nresults.\n