An Accelerated Gradient Tracking Algorithm with Projection Error for Distributed Optimization

Abstract

This paper investigates the problem of constrained distributed optimization solved by multi-agent network with on undirected graphs, which aims to optimize a global objective function consisting of the sum of local objective functions while only using local communication and computation. A distributed accelerated gradient tracking algorithm is proposed based on projection method. In addition, we introduce a projection error term and a corresponding auxiliary parameter in the algorithm to accelerate the convergence rate. The proposed algorithm enables faster convergence rate and improves convergence performance compared to other constrained distributed gradient algorithms. The efficiency and flexibility of the algorithm are illustrated by two simulation examples.