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Asymptotic convergence of constrained primal–dual dynamics

Cherukuri, Ashish and Mallada, Enrique and Cortés, Jorge (2016) Asymptotic convergence of constrained primal–dual dynamics. Systems and Control Letters, 87 . pp. 10-15. ISSN 0167-6911. doi:10.1016/j.sysconle.2015.10.006. https://resolver.caltech.edu/CaltechAUTHORS:20160218-130824812

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Abstract

This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.sysconle.2015.10.006DOIArticle
http://www.sciencedirect.com/science/article/pii/S0167691115002078PublisherArticle
http://arxiv.org/abs/1510.02150arXivDiscussion Paper
ORCID:
AuthorORCID
Cherukuri, Ashish0000-0002-7609-5080
Mallada, Enrique0000-0003-1568-1833
Additional Information:© 2015 Elsevier B.V.
Subject Keywords:Primal–dual dynamics; Constrained optimization; Saddle points; Discontinuous dynamics; Caratheodory solutions
DOI:10.1016/j.sysconle.2015.10.006
Record Number:CaltechAUTHORS:20160218-130824812
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160218-130824812
Official Citation:Ashish Cherukuri, Enrique Mallada, Jorge Cortés, Asymptotic convergence of constrained primal–dual dynamics, Systems & Control Letters, Volume 87, January 2016, Pages 10-15, ISSN 0167-6911, http://dx.doi.org/10.1016/j.sysconle.2015.10.006. (http://www.sciencedirect.com/science/article/pii/S0167691115002078)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64568
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Feb 2016 22:24
Last Modified:10 Nov 2021 23:32

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