Karl Heinz Borgwardt

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Karl-Heinz Borgwardt, Oberwolfach

Karl Heinz Borgwardt (* 1949 ) is a German mathematician who deals with optimization and operations research .

Borgwardt received his doctorate in 1977 at the University of Kaiserslautern under Helmut Brakhage (investigations into the asymptotics of the mean number of steps in simplex methods in linear optimization). He is a professor at the University of Augsburg .

In 1982 he received the Frederick W. Lanchester Prize . Borgwardt analyzed the simplex method using methods of stochastic geometry and was thus able to explain why the simplex method is so efficient in practice despite poor theoretical worst case behavior (proof of the mean polynomiality and sharp asymptotic limit values ​​for the number of pivot points to be expected) Steps).

Fonts

  • The Simplex Method, a probabilistic analysis, Springer 1987
  • Optimization, operations research, game theory. Mathematical basics, Birkhäuser 2001
  • with Matthias Tinkl, Thomas Wörle: collection of exercises and exam trainer for optimization, Vieweg, Teubner 2009
  • How fast does the simplex process normally work: or: Der Kampf um (stochastic independence), DMV Mitteilungen 2014, Issue 2, pp. 80–92
  • The Average Number of Pivot Steps Required by the Simplex-Method is Polynomial, Zeitschrift für Operations Research, Volume 7, 1982, No. 3, pp. 157-177
  • Some Distribution-Independent Results About the Asymptotic Order of the Average Number of Pivot Steps of the Simplex Method, Mathematics of Operations Research, Volume 7, 1982, No. 3, pp. 441-462
  • Probabilistic Analysis of Optimization-Algorithms - Some Aspects From a Practical Point of View, Acta Applicandae Mathematicae, Volume 10, 1987, pp. 171-210
  • A Sharp Upper Bound for the Expected Number of Shadow-Vertices in the Rotation-Symmetry-Model (Quadratic in the smaller and sublinear in the larger dimension of the LP), 1999 Mathematics of Operations Research, Vol. 24, No. 3, pp. 544-603 and (as a second print) Mathematics of Operations Research, Vol. 24, no. 4, pp. 925-984.
  • Probabilistic analysis of the Simplex method, in: Jeffrey Lagarias, M. Todd (Eds.), Mathematical Developments Arising from Linear Programming, Volume 114, 1990, pp. 21-34
  • Probabilistic Analysis Of Simplex Algorithms, in CA Floudas, PM Pardalos: Encyclopedia of Optimization, Volume 4, 2001, pp. 368-379

Web links

Individual evidence

  1. ↑ Karl Heinz Borgwardt in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
personal data
SURNAME Borgwardt, Karl Heinz
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH 1949