Computational Convergence Analysis of Distributed Optimization Algorithms for Directed Graphs

In this paper, we present a unified framework based on integral quadratic constraints for analyzing the convergence of distributed push-pull based optimization algorithms for directed graphs. Our framework provides numerical upper bounds on linear convergence rates of existing distributed push-pull...

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Vydáno v:IEEE International Conference on Control and Automation (Print) s. 1096 - 1101
Hlavní autoři: Zhang, Shengjun, Yi, Xinlei, George, Jemin, Yang, Tao
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.07.2019
Témata:
Automation
Convergence
Directed graphs
Linear programming
Optimization
Upper bound
ISSN:1948-3457
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Shrnutí:In this paper, we present a unified framework based on integral quadratic constraints for analyzing the convergence of distributed push-pull based optimization algorithms for directed graphs. Our framework provides numerical upper bounds on linear convergence rates of existing distributed push-pull based algorithms when local objective functions are strongly convex and smooth and directed graphs are strongly connected. Moreover, we propose a new distributed optimization algorithm for directed graphs and show that the proposed framework can also be applied to establish its linear convergence rate. The theoretical results are illustrated and validated via numerical examples.
ISSN:1948-3457
DOI:10.1109/ICCA.2019.8899565