Skip to main content
SpringerLink
Log in

An interactive algorithm for nonlinear vector optimization

  • Published:
Applied Mathematics and Optimization Submit manuscript

Abstract

In this paper an interactive algorithm for nonlinear vector optimization problems is presented. This algorithm decides, after solving only two optimization problems, whether or not there are efficient points in the feasible set. In the latter case, an efficient point depending on parameters is automatically computed, and (which is much more important) efficient points for each parameter can be calculated by this procedure.

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

Access this article

Log in via an institution

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

References

  1. Bitran GR, Magnanti TL (1979) The structure of admissible points with respect to cone dominance, J Optim Theory Appl 29:573–614

    Google Scholar 

  2. Brosowski B (1987) A criterion for efficiency and some applications. In: Brosowski B, Martensen E (eds) Optimization in Mathematical Physics. Lang, Frankfurt, pp 37–60

    Google Scholar 

  3. Brosowski B (1989) A recursive procedure for the solution of linear and nonlinear vector optimization problems. In: Eschenauer HA, Thierauf G. (eds) Discretization Methods and Structural Optimization—Procedures and Applications, Springer-Verlag, Berlin, pp 95–101.

    Google Scholar 

  4. Eschenauer H, Schäfer E (1987) Interaktive Vektoroptimierungsverfahren in der Strukturmechanik, Preprint, University Siegen

  5. Helbig S (1987) Parametric optimization with a bottleneck objective and vector optimization. In: Jahn J, Krabs W (eds) Recent Advances and Historical Development of Vector Optimization. Springer-Verlag, Berlin, pp 146–159

    Google Scholar 

  6. Helbig S (1990) An algorithm for quadratic vector optimization problems. Z Angew Math Mech 70, T625-T627

    Google Scholar 

  7. Köllner C (1987) Ein interaktives Verfahren zur Lösung finiter linearer Vektoroptimierungsprobleme. Diplomthesis, Frankfurt, 281 pp

    Google Scholar 

  8. Pascoletti A, Serafini P (1984) Scalarizing vector optimization problems. J Optim Theory Appl 42:499–524

    Google Scholar 

  9. Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

  10. Yu PL (1974) Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. J Optim Theory Appl 14:319–377

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Strasse 6-10, D-6000, Frankfurt/Main, West Germany

    Siegfried Helbig

Authors
  1. Siegfried Helbig
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. Stoer

Rights and permissions

Reprints and permissions

About this article

Cite this article

Helbig, S. An interactive algorithm for nonlinear vector optimization. Appl Math Optim 22, 147–151 (1990). https://doi.org/10.1007/BF01447324

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01447324

Keywords

Search

Navigation