A hybrid control framework for fast methods under invexity

Non-Zeno trajectories with exponential rate

Conference paper (2018)

Authors

Arman Sharifi K. Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering
T. Keviczky Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering
Research Group
Team Tamas Keviczky (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2018 Arman Sharifi K., P. Mohajerin Esfahani, T. Keviczky
DOI: https://doi.org/10.1109/CDC.2018.8618707
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Published Date

2018

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Tamas Keviczky

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.

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