A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate

A. Sharifi Kolarijani; P. Mohajerin Esfahani; T. Keviczky

doi:10.1109/CDC.2018.8618707

A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate

A. Sharifi Kolarijani, P. Mohajerin Esfahani, T. Keviczky

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In this paper, we propose a framework to design a class of fast gradient-based methods in continuous-time that, in comparison with the existing literature including Nesterov's fast-gradient method, features a state-dependent, time-invariant damping term that acts as a feedback control input. The proposed design scheme allows for a user-defined, exponential rate of convergence for a class of nonconvex, unconstrained optimization problems in which the objective function satisfies the so-called Polyak-Łojasiewicz inequality. Formulating the optimization algorithm as a hybrid control system, a state-feedback input is synthesized such that a desired rate of convergence is guaranteed. Furthermore, we establish that the solution trajectories of the hybrid control system are Zeno-free.

Original language	English
Title of host publication	Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)
Editors	Andrew R. Teel, Magnus Egerstedt
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	4078-4083
ISBN (Electronic)	978-1-5386-1395-5
DOIs	https://doi.org/10.1109/CDC.2018.8618707
Publication status	Published - 2018
Event	CDC 2018: 57th IEEE Conference on Decision and Control - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Conference

Conference	CDC 2018: 57th IEEE Conference on Decision and Control
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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A_Hybrid_Control_Framework_for_Fast_Methods_Under_Invexity_Non-Zeno_Trajectories_with_Exponential_RateFinal published version, 363 KB

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title = "A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate",

abstract = "In this paper, we propose a framework to design a class of fast gradient-based methods in continuous-time that, in comparison with the existing literature including Nesterov's fast-gradient method, features a state-dependent, time-invariant damping term that acts as a feedback control input. The proposed design scheme allows for a user-defined, exponential rate of convergence for a class of nonconvex, unconstrained optimization problems in which the objective function satisfies the so-called Polyak-{\L}ojasiewicz inequality. Formulating the optimization algorithm as a hybrid control system, a state-feedback input is synthesized such that a desired rate of convergence is guaranteed. Furthermore, we establish that the solution trajectories of the hybrid control system are Zeno-free.",

author = "{Sharifi Kolarijani}, A. and {Mohajerin Esfahani}, P. and T. Keviczky",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; CDC 2018: 57th IEEE Conference on Decision and Control ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2018",

doi = "10.1109/CDC.2018.8618707",

language = "English",

pages = "4078--4083",

editor = "Teel, {Andrew R. } and Egerstedt, {Magnus }",

booktitle = "Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)",

publisher = "IEEE",

address = "United States",

}

Sharifi Kolarijani, A , Mohajerin Esfahani, P & Keviczky, T 2018, A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate. in AR Teel & M Egerstedt (eds), Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018). IEEE, Piscataway, NJ, USA, pp. 4078-4083, CDC 2018: 57th IEEE Conference on Decision and Control, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8618707

A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate. / Sharifi Kolarijani, A.; Mohajerin Esfahani, P.; Keviczky, T.
Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018). ed. / Andrew R. Teel; Magnus Egerstedt. Piscataway, NJ, USA: IEEE, 2018. p. 4078-4083.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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AB - In this paper, we propose a framework to design a class of fast gradient-based methods in continuous-time that, in comparison with the existing literature including Nesterov's fast-gradient method, features a state-dependent, time-invariant damping term that acts as a feedback control input. The proposed design scheme allows for a user-defined, exponential rate of convergence for a class of nonconvex, unconstrained optimization problems in which the objective function satisfies the so-called Polyak-Łojasiewicz inequality. Formulating the optimization algorithm as a hybrid control system, a state-feedback input is synthesized such that a desired rate of convergence is guaranteed. Furthermore, we establish that the solution trajectories of the hybrid control system are Zeno-free.

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ER -

A hybrid control framework for fast methods under invexity: Non-Zeno trajectories with exponential rate

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