2021/04/24 by Wei Jiang, Jiang, Wei, Andreas Grammenos +5 · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Technologies #Cooperative Communication and Network Coding #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Parallel #Sparse and Compressive Sensing Techniques #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2104.11866
openalex publication_date 2021/04/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology (directed graph or digraph). First, we reformulate the optimization problem so that Alternating Direction Method of Multipliers (ADMM) can be utilized. Then, we propose an algorithm, herein called Asynchronous Approximate Distributed Alternating Direction Method of Multipliers (AsyAD-ADMM), using finite-time asynchronous approximate ratio consensus, to solve the multi-node convex optimization problem, in which every node performs iterative computations and exchanges information with its neighbors asynchronously. More specifically, at every iteration of AsyAD-ADMM, each node solves a local convex optimization problem for one of the primal variables and utilizes a finite-time asynchronous approximate consensus protocol to obtain the value of the other variable which is close to the optimal value, since the cost function for the second primal variable is not decomposable. If the individual cost functions are convex but not necessarily differentiable, the proposed algorithm converges at a rate of O(1/k), where k is the iteration counter. The efficacy of AsyAD-ADMM is exemplified via a proof-of-concept distributed least-square optimization problem with different performance-influencing factors investigated.