An Improved Distributed Nesterov Gradient Tracking Algorithm for Smooth Convex Optimization Over Directed Networks

Abstract

This article explores the problem of distributed optimization for functions that are smooth and nonstrongly convex over directed networks. To address this issue, an improved distributed Nesterov gradient tracking (IDNGT) algorithm is proposed, which utilizes the adapt-then-combine rule and row-stochastic weights. A main novelty of the proposed algorithm is the introduction of a scale factor into the gradient tracking scheme to suppress the consensus error. By the estimate sequence approach, the dynamics of the error due to the unbalance of directed networks is analyzed and it is shown that a sublinear convergence rate can be achieved with a vanishing step size. Numerical results suggest that the performance of IDNGT is comparable to that of the centralized Nesterov gradient descent algorithm.