Continuous-Time Optimization of Time-Varying Cost Functions Via Finite-Time Stability with Pre-Defined Convergence Time. Romero, O. & Benosman, M. abstract bibtex 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.
@article{romero_continuous-time_nodate,
title = {Continuous-{Time} {Optimization} of {Time}-{Varying} {Cost} {Functions} {Via} {Finite}-{Time} {Stability} with {Pre}-{Defined} {Convergence} {Time}},
abstract = {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.},
language = {en},
author = {Romero, Orlando and Benosman, Mouhacine},
pages = {6},
}
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