Abstract
This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.
Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 1023-1029 |
Number of pages | 7 |
ISBN (Electronic) | 9781509018376 |
DOIs | |
State | Published - Dec 27 2016 |
Externally published | Yes |
Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |
Other
Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country/Territory | United States |
City | Las Vegas |
Period | 12/12/16 → 12/14/16 |
ASJC Scopus subject areas
- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization