Contraction and Robustness of Continuous Time Primal-Dual Dynamics
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Author(s)
Nguyen, Hung D.
Vu, Thanh Long
Turitsyn, Konstantin
Slotine, Jean-Jacques E
Date Issued
October 2018
Journal
IEEE Control Systems Letters
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Nguyen, Hung D. et al. “Contraction and Robustness of Continuous Time Primal-Dual Dynamics.” IEEE Control Systems Letters 2, 4 (October 2018): 755–760. © 2017 IEEE
Version
Author's final manuscript
Abstract
The Primal-dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This letter focuses on continuous, possibly non-autonomous PD dynamics arising in a network context, in distributed optimization, or in systems with multiple time-scales. We show that the PD algorithm is indeed strictly contracting in specific metrics and analyze its robustness establishing stability and performance guarantees for different approximate PD systems. We derive estimates for the performance of multiple time-scale multi-layer optimization systems, and illustrate our results on a PD representation of the Automatic Generation Control of power systems.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/lcsys.2018.2847408
