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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Bibliographic Details
Published in:IEEE International Conference on Control and Automation (Print) pp. 1096 - 1101
Main Authors: Zhang, Shengjun, Yi, Xinlei, George, Jemin, Yang, Tao
Format: Conference Proceeding
Language:English
Published: IEEE 01.07.2019
Subjects:
Automation
Convergence
Directed graphs
Linear programming
Optimization
Upper bound
ISSN:1948-3457
Online Access:Get full text
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Summary: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