Skip to main content
Log in

A note on minimization problems and multistep methods

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary.

We use the qualitative properties of the solution flow of the gradient equation \(\dot{x} = - \nabla f(x)\) to compute a local minimum of a real-valued function \(f\). 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 \(A(\alpha )\)-stable formulae this leads to an efficient solver for stiff minimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received July 10, 1995 / Revised version received June 27, 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schropp, J. A note on minimization problems and multistep methods. Numer. Math. 78, 87–101 (1997). https://doi.org/10.1007/s002110050305

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002110050305

Navigation