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
ISBN (Electronic)978-1-5386-1395-5
Publication statusPublished - 2018
EventCDC 2018: 57th IEEE Conference on Decision and Control - Miami, United States
Duration: 17 Dec 201819 Dec 2018


ConferenceCDC 2018: 57th IEEE Conference on Decision and Control
CountryUnited States

ID: 51914802