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

Titelangaben

Grüne, Lars ; Karafyllis, Iasson:
Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.
In: Hüper, Knut ; Trumpf, Jochen (Hrsg.): Mathematical System Theory : Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday. - S.l. : CreateSpace Independent Publishing Platform , 2013 . - S. 183-210

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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.