2024/07/23 by Khatana, Vivek, Salapaka, Murti V.
#Artificial Intelligence (cs.AI) #Distributed #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Parallel #Systems and Control (eess.SY) #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2407.16728
In this article, we focus on solving a class of distributed optimization problems involving n agents with the local objective function at every agent i given by the difference of two convex functions fi and gi (difference-of-convex (DC) form), where fi and gi are potentially nonsmooth. The agents communicate via a directed graph containing n nodes. We create smooth approximations of the functions fi and gi and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.