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Semi-global exponential stability of augmented primal–dual gradient dynamics for constrained convex optimization

Tang, Yujie and Qu, Guannan and Li, Na (2020) Semi-global exponential stability of augmented primal–dual gradient dynamics for constrained convex optimization. Systems and Control Letters, 144 . Art. No. 104754. ISSN 0167-6911. https://resolver.caltech.edu/CaltechAUTHORS:20200825-101337874

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Abstract

Primal–dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal–dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.sysconle.2020.104754DOIArticle
ORCID:
AuthorORCID
Tang, Yujie0000-0002-4921-8372
Additional Information:© 2020 Elsevier B.V. Received 8 October 2019, Revised 18 May 2020, Accepted 17 July 2020, Available online 25 August 2020. This work was supported by NSF 1608509, NSF CAREER 1553407, AFOSR YIP, and ONR YIP.
Funders:
Funding AgencyGrant Number
NSFECCS-1608509
NSFECCS-1553407
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Constrained optimization; Primal–dual dynamics; Exponential stability
Record Number:CaltechAUTHORS:20200825-101337874
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200825-101337874
Official Citation:Yujie Tang, Guannan Qu, Na Li, Semi-global exponential stability of augmented primal–dual gradient dynamics for constrained convex optimization, Systems & Control Letters, Volume 144, 2020, 104754, ISSN 0167-6911, https://doi.org/10.1016/j.sysconle.2020.104754. (http://www.sciencedirect.com/science/article/pii/S0167691120301365)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105099
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Aug 2020 17:17
Last Modified:25 Aug 2020 17:17

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