Stability of primal-dual gradient dynamics and applications to network optimization

@article{Feijer2010StabilityOP,
  title={Stability of primal-dual gradient dynamics and applications to network optimization},
  author={Diego Feijer and Fernando Paganini},
  journal={Automatica},
  year={2010},
  volume={46},
  pages={1974-1981}
}
This paper considers dynamic laws that seek a saddle point of a function of two vector variables, bymoving each in the direction of the corresponding partial gradient. This method has old roots in the classical work of Arrow, Hurwicz and Uzawa on convex optimization, and has seen renewed interest with its recent application to resource allocation in communicationnetworks. This paper brings other tools to bear on this problem, in particular Krasovskii’s method to find Lyapunov functions, and… CONTINUE READING
Highly Influential
This paper has highly influenced 17 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 225 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 117 extracted citations

Resilient Distributed DC Optimal Power Flow Against Data Integrity Attack

IEEE Transactions on Smart Grid • 2018
View 8 Excerpts
Method Support
Highly Influenced

Improving the Performance of Network Congestion Control Algorithms

IEEE Transactions on Automatic Control • 2015
View 5 Excerpts
Method Support
Highly Influenced

A distributed PID controller for network congestion control problems

2014 American Control Conference • 2014
View 4 Excerpts
Highly Influenced

On the Exponential Stability of Primal-Dual Gradient Dynamics

IEEE Control Systems Letters • 2019
View 9 Excerpts
Highly Influenced

An Optimal and Distributed Feedback Voltage Control Under Limited Reactive Power

2018 Power Systems Computation Conference (PSCC) • 2018
View 5 Excerpts
Highly Influenced

226 Citations

0204060'12'14'16'18
Citations per Year
Semantic Scholar estimates that this publication has 226 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 17 references

Studies in linear and non-linear programming

K. Arrow, L. Hurwicz, H. Uzawa
1958
View 20 Excerpts
Highly Influenced

The mathematics of internet congestion control

R. 205–228. Srikant
2004
View 4 Excerpts
Highly Influenced

Problems of the theory of stability of motion

H K.
Research Society, • 1996
View 4 Excerpts
Highly Influenced

Krasovskii's method in the stability of network control

2009 American Control Conference • 2009
View 3 Excerpts

Utility-optimal random-access control

IEEE Transactions on Wireless Communications • 2007
View 3 Excerpts