Corpus ID: 36488818

# On the Linear Convergence of Distributed Optimization over Directed Graphs

@article{Xi2015OnTL,
title={On the Linear Convergence of Distributed Optimization over Directed Graphs},
author={Chenguang Xi and Usman A. Khan},
journal={arXiv: Optimization and Control},
year={2015}
}
• Published 2015
• Mathematics
• arXiv: Optimization and Control
• This paper develops a fast distributed algorithm, termed \emph{DEXTRA}, to solve the optimization problem when~$n$ agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a~\emph{directed} graph. Existing algorithms solve the problem restricted to directed graphs with convergence rates of $O(\ln k/\sqrt{k})$ for general convex objective functions and $O(\ln k/k)$ when the… CONTINUE READING

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 38 CITATIONS, ESTIMATED 91% COVERAGE

## Linear Convergence in Optimization Over Directed Graphs With Row-Stochastic Matrices

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## Fast distributed optimization over directed graphs

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## Gradient-Consensus Method for Distributed Optimization in Directed Networks.

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• 2017 International Workshop on Complex Systems and Networks (IWCSN)
• 2017

## DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs

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### CITATION STATISTICS

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 45 REFERENCES

## EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization

• Computer Science, Mathematics
• SIAM J. Optim.
• 2015
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## Distributed Subgradient Projection Algorithm Over Directed Graphs

• Mathematics, Computer Science
• IEEE Transactions on Automatic Control
• 2017
VIEW 1 EXCERPT

## Distributed optimization over time-varying directed graphs

• Computer Science, Mathematics
• 52nd IEEE Conference on Decision and Control
• 2013
VIEW 1 EXCERPT

## On the Convergence of Decentralized Gradient Descent

• Mathematics, Computer Science
• SIAM J. Optim.
• 2016
VIEW 3 EXCERPTS

## On the distributed optimization over directed networks

• Mathematics, Computer Science
• Neurocomputing
• 2017

## Graph balancing for distributed subgradient methods over directed graphs

• Mathematics, Computer Science
• 2015 54th IEEE Conference on Decision and Control (CDC)
• 2015
VIEW 1 EXCERPT

## Distributed Gradient Descent over Directed Graphs

• Mathematics
• 2015
VIEW 2 EXCERPTS

## Constrained Consensus and Optimization in Multi-Agent Networks

• Computer Science, Mathematics
• IEEE Transactions on Automatic Control
• 2010
VIEW 1 EXCERPT

## Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

• Computer Science, Mathematics
• IEEE Transactions on Automatic Control
• 2012
VIEW 1 EXCERPT

## On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

• Computer Science, Mathematics
• IEEE Transactions on Signal Processing
• 2014