A Distributed Optimization Accelerated Algorithm with Uncoordinated Time-Varying Step-Sizes in an Undirected Network

Yunshan Lü, Hailing Xiong, Hao Zhou and Xin Guan
Additional contact information
Yunshan Lü: Database and Artificial Intelligence Laboratory, College of Computer and Information Science, Southwest University, Chongqing 400715, China
Hailing Xiong: Database and Artificial Intelligence Laboratory, College of Computer and Information Science, Southwest University, Chongqing 400715, China
Hao Zhou: Database and Artificial Intelligence Laboratory, College of Computer and Information Science, Southwest University, Chongqing 400715, China
Xin Guan: Database and Artificial Intelligence Laboratory, College of Computer and Information Science, Southwest University, Chongqing 400715, China

Mathematics, 2022, vol. 10, issue 3, 1-17

Abstract: In recent years, significant progress has been made in the field of distributed optimization algorithms. This study focused on the distributed convex optimization problem over an undirected network. The target was to minimize the average of all local objective functions known by each agent while each agent communicates necessary information only with its neighbors. Based on the state-of-the-art algorithm, we proposed a novel distributed optimization algorithm, when the objective function of each agent satisfies smoothness and strong convexity. Faster convergence can be attained by utilizing Nesterov and Heavy-ball accelerated methods simultaneously, making the algorithm widely applicable to many large-scale distributed tasks. Meanwhile, the step-sizes and accelerated momentum coefficients are designed as uncoordinate, time-varying, and nonidentical, which can make the algorithm adapt to a wide range of application scenarios. Under some necessary assumptions and conditions, through rigorous theoretical analysis, a linear convergence rate was achieved. Finally, the numerical experiments over a real dataset demonstrate the superiority and efficacy of the novel algorithm compared to similar algorithms.

Keywords: distributed convex optimization; accelerated method; uncoordinated; undirected network; linear convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/3/357/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/3/357/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:3:p:357-:d:732834

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().