2015/04/09 by Ye Pu, Pu, Ye, Melanie N. Zeilinger +3 · 4 citations
Computer Science · Engineering · Mathematics · #Algorithm #Bounded function #Channel (broadcasting) #Computer science #Convergence (economics) #Distributed Control Multi-Agent Systems #Distributed algorithm #Distributed computing #FOS: Electrical engineering #FOS: Mathematics #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Optimization problem #Quantization (signal processing) #Rate of convergence #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1504.02317
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a limited data-rate. A common technique to address the latter limitation is to apply quantization to the exchanged information. We propose two distributed optimization algorithms with an iteratively refining quantization design based on the inexact proximal gradient method and its accelerated variant. We show that if the parameters of the quantizers, i.e. the number of bits and the initial quantization intervals, satisfy certain conditions, then the quantization error is bounded by a linearly decreasing function and the convergence of the distributed algorithms is guaranteed. Furthermore, we prove that after imposing the quantization scheme, the distributed algorithms still exhibit a linear convergence rate, and show complexity upper-bounds on the number of iterations to achieve a given accuracy. Finally, we demonstrate the performance of the proposed algorithms and the theoretical findings for solving a distributed optimal control problem.