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

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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 languageEnglish
Title of host publicationProceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)
EditorsAndrew R. Teel, Magnus Egerstedt
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Pages4078-4083
ISBN (Electronic)978-1-5386-1395-5
DOIs
Publication statusPublished - 2018
EventCDC 2018: 57th IEEE Conference on Decision and Control - Miami, United States
Duration: 17 Dec 201819 Dec 2018

Conference

ConferenceCDC 2018: 57th IEEE Conference on Decision and Control
CountryUnited States
CityMiami
Period17/12/1819/12/18

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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