Continuous-Time Optimization of Time-Varying Cost Functions via Finite-Time Stability with Pre-Defined Convergence Time

In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a w...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the American Control Conference pp. 88 - 93
Main Authors: Romero, Orlando, Benosman, Mouhacine
Format: Conference Proceeding
Language:English
Published: AACC 01.07.2020
Subjects:
Acceleration
Convergence
Cost function
Heuristic algorithms
Modeling
Stability analysis
ISSN:2378-5861
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.
ISSN:2378-5861
DOI:10.23919/ACC45564.2020.9147809