Distributed Optimization in an Energy-Constrained Network Using a Digital Communication Scheme

摘要

We consider a distributed optimization problem where n nodes, S-I, I/in(1,...,n), wish to minimize a common strongly convex function f(x),x= x(underline)1, ...,x(underline)(caret)T, and suppose that node S-I only has control of variable x-I. The nodes locally update their respective variables and periodically exchange their values over noisy channels. Previous studies of this problem have mainly focused on the convergence issue and the analysis of convergence rate. In this work, we focus on the communication energy and study its impact on convergence. In particular, we study the minimum amount of communication energy required for nodes to obtain an /epsilon-minimizer of f(x) in the mean square sense.