DCDistADMM: ADMM Algorithm for Contsrained Distributed Optimization over Directed Graphs
Abstract
This article focuses on multiagent distributed optimization problems with a common decision variable, a global linear equality constraint, and local set constraints over directed interconnection topologies. We propose a novel ADMM based distributed algorithm to solve the above problem. During every iteration of the algorithm, each agent solves a local convex optimization problem and utilizes a finitetime ``approximate'' consensus protocol to update its local estimate of the optimal solution. The proposed algorithm is the first ADMM based algorithm with convergence guarantees to solve distributed multiagent optimization problems where the interconnection topology is directed. We establish two strong explicit convergence rate estimates for the proposed algorithm to the optimal solution under two different sets of assumptions on the problem data. Further, we evaluate our proposed algorithm by solving two nonlinear and nondifferentiable constrained distributed optimization problems over directed graphs. Additionally, we provide a numerical comparison of the proposed algorithm with other stateoftheart algorithms to show its efficacy over the existing methods in the literature.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.13742
 Bibcode:
 2020arXiv200313742K
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control
 EPrint:
 18 pages, 9 Figures, includes an appendix