A note on minimization problems and multistep methods |
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Authors: | J. Schropp |
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Affiliation: | (1) Department of Mathematics, University of Konstanz, P.O. Box 5560, D-78434 Konstanz, Germany , DE |
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Abstract: | Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 34C35 49A21 65L05 65L20 |
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