Contraction and Robustness of Continuous Time Primal-Dual Dynamics
Author(s)
Nguyen, Hung D.; Vu, Thanh Long; Turitsyn, Konstantin; Slotine, Jean-Jacques E
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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.
Date issued
2018-10Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
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
ISSN
2475-1456
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