Contraction and Robustness of Continuous Time Primal-Dual Dynamics
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 arisi...
| Main Authors: | , , , |
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| Format: | Article |
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Institute of Electrical and Electronics Engineers (IEEE)
2020
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| Online Access: | https://hdl.handle.net/1721.1/128498 |
| _version_ | 1826207336066187264 |
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| author | Nguyen, Hung D. Vu, Thanh Long Turitsyn, Konstantin Slotine, Jean-Jacques E |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Nguyen, Hung D. Vu, Thanh Long Turitsyn, Konstantin Slotine, Jean-Jacques E |
| author_sort | Nguyen, Hung D. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:47:44Z |
| format | Article |
| id | mit-1721.1/128498 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:47:44Z |
| publishDate | 2020 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1284982022-09-28T16:17:09Z Contraction and Robustness of Continuous Time Primal-Dual Dynamics Nguyen, Hung D. Vu, Thanh Long Turitsyn, Konstantin Slotine, Jean-Jacques E Massachusetts Institute of Technology. Department of Mechanical Engineering 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. NSF (Awards 1554171 and 1550015) 2020-11-16T22:39:51Z 2020-11-16T22:39:51Z 2018-10 2019-01-03T15:02:29Z Article http://purl.org/eprint/type/JournalArticle 2475-1456 https://hdl.handle.net/1721.1/128498 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 http://dx.doi.org/10.1109/lcsys.2018.2847408 IEEE Control Systems Letters Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Nguyen, Hung D. Vu, Thanh Long Turitsyn, Konstantin Slotine, Jean-Jacques E Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title | Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title_full | Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title_fullStr | Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title_full_unstemmed | Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title_short | Contraction and Robustness of Continuous Time Primal-Dual Dynamics |
| title_sort | contraction and robustness of continuous time primal dual dynamics |
| url | https://hdl.handle.net/1721.1/128498 |
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