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Practical finite pivoting rules for the simplex method

Zusammenfassung

Pivot-Regeln sind ein wesentliches Element der Simplexmethode. In dieser Arbeit stellen wir zwei Varianten von Pivot-Regeln des „Bland'schen Typs“ vor. Während die Bland-Regel auf einer Indizierung der Variablen beruht, arbeiten die neuen Regeln mit sogenannten „Pivoting-Indices“, denen eine geometrische Bedeutung zukommt. Aufgrund dieser geometrischen Philosophie und durch Testrechnungen gestützt, erweisen sich diese Regeln nicht nur als einfach und endlich, sondern auch als vielversprechend für den praktischen Einsatz.

Summary

A pivoting rule is crucial to the simplex method. This paper suggests two variants of “Bland's type” of pivoting rule. In contrast with the latter, which are based on indices of variables, the new rules are based on so-called “pivoting indices”, which are of full geometrical meaning. According to the underlying geometric philosophy of them and test results obtained by the author, these rules are not only finite and simple, but also promising practically.

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Additional information

This work was performed in part while the author was visiting the Department of Mathematics, University of Washington, Seattle, USA

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Pan, P.-. Practical finite pivoting rules for the simplex method. OR Spektrum 12, 219–225 (1990). https://doi.org/10.1007/BF01721801

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Keywords

  • Geometrical Meaning
  • Simplex Method