A distributed accelerated optimization algorithm over time‐varying directed graphs with uncoordinated step‐sizes. (21st March 2022)

• Record Type: Journal Article
• Authors: Ran, Liang; Wang, Chengbo; Zheng, Lifeng; Li, Huaqing; Wang, Zheng
• Is Part Of: Optimal control applications and methods. Volume 43:Number 4(2022)
• Page Start: 1182
• Page End: 1200
• Publication Date: 2022-03-21
• Subjects: distributed optimization -- heavy‐ball method -- linear convergence -- multi‐agent systems -- time‐varying directed graphs; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2886
• Languages: English
• ISSNs: 0143-2087

Abstract

Abstract: This article proposes a distributed accelerated algorithm for solving distributed optimization problems which are defined in a time‐varying directed network. Different from the existing algorithms, by implementing row‐ and column‐stochastic matrices, this work eliminates the conservatism in the related work due to doubly‐stochastic matrices, and do not required estimate the Perron eigenvector of a stochastic matrix. Assuming that the global objective function is strongly convex and the gradient of each local objective function is Lipschitz‐continuous, it is proved that the algorithm converges linearly to the global optimization solution with proper uncoordinated step‐sizes and momentum parameters. The numerical simulations are utilized to verify the correctness of the theoretical results and show the practicability of the proposed algorithm.