2018/09/04 by Gesualdo Scutari, Ying Sun, Scutari, Gesualdo +1 · 10 citations
Computer Science · Engineering · #Distributed #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Mathematics #Multiagent Systems (cs.MA) #Optimization and Control (math.OC) #Parallel #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1809.01106
openalex publication_date 2018/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex (nonseparable) function--the agent's sum-utility--plus a Difference-of-Convex (DC) function (with nonsmooth convex part). This general formulation arises in many applications, from statistical machine learning to engineering. The proposed distributed method combines successive convex approximation techniques with a judiciously designed perturbed push-sum consensus mechanism that aims to track locally the gradient of the (smooth part of the) sum-utility. Sublinear convergence rate is proved when a fixed step-size (possibly different among the agents) is employed whereas asymptotic convergence to stationary solutions is proved using a diminishing step-size. Numerical results show that our algorithms compare favorably with current schemes on both convex and nonconvex problems.