Skip to main content
Springer Nature Link
Log in

On the choice of the pivot columns of the Simplex-method: Gradient criteria

Zur Auswahl der Pivotspalten beim Simplexalgorithmus: Gradienten-Kriterien

  • Contributed Papers
  • Published:
Computing Aims and scope Submit manuscript

Abstract

In a Monte Carlo simulation experiment we test 31 gradient pivot choice criteria for the Simplex-method. Among the several used norms we look for the one, which is best relative to the required number of iterations and computing time. Especially the goodness of the (most used) steepest unit ascent method is analysed and compared with the results of other criteria.

Zusammenfassung

Im Rahmen einer Monte-Carlo-Simulationsstudie werden 31 Gradienten-Kriterien zur Auswahl der Pivotspalten beim Simplex-algorithmus getestet. Unter den dabei zugrunde gelegten Normen wird diejenige bestimmt, die bezüglich der benötigten Anzahl von Iterationsschritten und der verbrauchten Rechenzeit optimal ist. Insbesondere wird die Güte des (gebräuchlichsten) Kriteriums des steilsten Anstiegs untersucht und mit den Resultaten anderer Kriterien verglichen.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Abel, P.: Eine Untersuchung zur zufälligen Auswahl der Pivotspalten bei Simplexalgorithmus. Manuskript (1984).

  2. Abel, P., Thiel, R.: Mehrstufige stochastische Produktionsmodelle. Frankfurt a. M.: Fischer 1981.

    Google Scholar 

  3. Dantzig, G. B.: Lineare Programmierung und Erweiterungen. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  4. Goldfarb, D., Reid, J. K.: A practicable steepest edge simplex algorithm. Math. Programming12, 361–371 (1977).

    Article  Google Scholar 

  5. Harwell: Harwell subroutine library. Oxfordshire: AERE Harwell 1980.

    Google Scholar 

  6. IMSL: IMSL library reference manual 1–3. Houston: IMSL 1980.

    Google Scholar 

  7. Knuth, D. E.: The art of computer programming 2: Seminumerical algorithms. Reading, Mass.: Addison-Wesley 1969.

    Google Scholar 

  8. Kuhn, H. W., Quandt, R. E.: An experimental study of the simplex method. Proc. Symposia in Appl. Math.15, 107–124 (1963).

    Google Scholar 

  9. Quandt, R. E., Kuhn, H. W.: On some computer experiments in linear programming. Bulletin de l'Institut International de Statistique39, 363–372 (1962).

    Google Scholar 

  10. Quandt, R. E., Kuhn, H. W.: On upper bounds for the number of iterations in solving linear programs. Operations Research12, 161–165 (1964).

    Google Scholar 

  11. SAS/OR: Operations Research user's guide: Cary: SAS Institute 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Gartenstrasse 73, D-6908, Wiesloch, Federal Republic of Germany

    P. Abel

Authors
  1. P. Abel
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abel, P. On the choice of the pivot columns of the Simplex-method: Gradient criteria. Computing 38, 13–21 (1987). https://doi.org/10.1007/BF02253740

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02253740

AMS Subject Classification

Key words