Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.

Lars Grüne 1 Iasson Karafyllis 2
1 Mathematisches Institut [Bayreuth]
2 Department of Environmental Engineering - Grèce
Abstract : We present and analyze an abstract step size selection algorithm which ensures asymptotic stability of numerical approximations to asymptotically stable ODEs. A particular implementation of this algorithm is proposed and tested with two numerical examples. The application to ODEs solving nonlinear optimization problems on manifolds is explained and illustrated by means of the Rayleigh flow for computing eigenvalues of symmetric matrices.
Type de document :
Chapitre d'ouvrage
K. Hüper and J. Trumpf. Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, CreateSpace, pp.183 - 210, 2013, 978-1470044008
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https://hal.inria.fr/hal-00800458
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 13 mars 2013 - 16:39:09
Dernière modification le : lundi 21 mars 2016 - 11:30:02

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Lars Grüne, Iasson Karafyllis. Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.. K. Hüper and J. Trumpf. Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, CreateSpace, pp.183 - 210, 2013, 978-1470044008. <hal-00800458>

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