Skip to main content
Log in

A trajectory-following method for unconstrained optimization

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.

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.

Similar content being viewed by others

References

  1. Brown, A. A.,Numerical Experience with Trajectory Following Methods for Unconstrained Optimization, Technical Report No. 154, Hattfield Polytechnic, 1985.

  2. Brown, A. A., andBartholomew-Biggs, M. C.,Some Effective Methods for Unconstrained Optimization Based on the Solution of Systems of Ordinary Differential Equations, Journal of Optimization Theory and Applications, Vol. 62, No. 2, pp. 211–224, 1989.

    Google Scholar 

  3. Snyman, J. A., andFatti, L. P.,Multi-Start Global Minimization Algorithm with Dynamic Search Trajectories, Journal of Optimization Theory and Applications, Vol. 54, No. 1, pp. 121–141, 1987.

    Google Scholar 

  4. Walter, W.,Gewöhnliche Differentialgleichungen, Springer-Verlag, Berlin, Germany, 1972.

    Google Scholar 

  5. Schachtner, R., Private Communication, 1988.

  6. Schwarz, H. R.,Numerische Mathematik, B. G. Teubner, Stuttgart, Germany, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by O. L. Mangasarian

The work of the second author was supported by the DFG Schwerpunkt “Anwendungs-bezogene Optimierung and Steuerung.”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schäffler, S., Warsitz, H. A trajectory-following method for unconstrained optimization. J Optim Theory Appl 67, 133–140 (1990). https://doi.org/10.1007/BF00939739

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00939739

Key Words

Navigation