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On the variance of the number of pivot steps required by the simplex algorithm

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Abstract

The article provides an asymptotic probabilistic analysis of the variance of the number of pivot steps required by phase II of the “shadow vertex algorithm” — a parametric variant of the simplex algorithm, which has been proposed by Borgwardt [1]. The analysis is done for data which satisfy a rotationally invariant distribution law in then-dimensional unit ball.

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References

  1. Borgwardt KH (1987) The simplex method — A probabilistic analysis. Springer New York Berlin Heidelberg

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  2. Feller W (1960, 1966) An introduction to probability and its applications, Vol I–II. Wiley New York

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  3. Küfer KH (1992) Asymptotische Varianzanalysen in der stochastischen Polyedertheorie. Dissertation, Universität Kaiserslautern

  4. Raynaud H (1970) Sur l'enveloppe convexe des nuages de points aléatoires dans ℝn. J Appl Prob 7:35–48

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  5. Shamir R (1987) The efficiency of the simplex method: A survey. Management Science 33:241–262

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Authors and Affiliations

  1. Dept. of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Str., P.O. Box 3049, 67663, Kaiserslautern, Germany

    Karl-Heinz Küfer

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  1. Karl-Heinz Küfer
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Küfer, KH. On the variance of the number of pivot steps required by the simplex algorithm. ZOR - Methods and Models of Operations Research 42, 1–24 (1995). https://doi.org/10.1007/BF01415671

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  • DOI: https://doi.org/10.1007/BF01415671

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