Markus G?hl and Karl-Heinz Borgwardt
The average number of pivot steps of the simplex-algorithm based on a generalized rotation-symmetry-model
preprint (2014)
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Auch erschienen in: Mathematical Methods of Operations Research, Volume 80, Issue 3 (2014),p. 329-366. DOI https://doi.org/10.1007/s00186-014-0483-8

Karl-Heinz Borgwardt
Wie schnell arbeitet das Simplexverfahren normalerweise? Oder: das Streben nach (stochastischer) Unabh?ngigkeit
Mitteilungen der Deutschen Mathematiker-Vereinigung 22, 80-92 (2014)
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Karl-Heinz Borgwardt
Aufgabensammlung und Klausurentrainer zur Optimierung : Für die Bachelorausbildung in mathematischen Studieng?ngen
(2010)
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Operations Research Proceedings 2008: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR) 伟德国际_伟德国际1946$娱乐app游戏 of Augsburg, September 3-5, 2008
in: , ed. by Bernhard Fleischmann, Karl-Heinz Borgwardt, Robert Klein, Axel Tuma, (Springer: Berlin [u.a.], 2009)
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Karl-Heinz Borgwardt
Average-case analysis of the double description method and the beneath-beyond algorithm
Discrete & Computational Geometry 37, 175-204 (2007)
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Karl-Heinz Borgwardt
Die mittlere Schrittzahl beim Simplexverfahren - als vorlesbare Vereinfachung
in: , (2004)
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Petra Huhn and Karl-Heinz Borgwardt
Interior-point methods: worst case and average case analysis of a phase-I algorithm and a termination procedure
Journal of Complexity 18, 833-910 (2002)
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Karl-Heinz Borgwardt
Linear programming
in: Knowledge for sustainable development: an insight into the encyclopedia of life support systems, (Environment and Development series) 283-318 (UNESCO/EOLSS: Paris, 2002)
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Contributions to Theme 2.2 "Optimization and Operations Research"

Karl-Heinz Borgwardt
Optimierung, Operations Research, Spieltheorie : mathematische Grundlagen
(Birkh?user: Basel [u.a.], 2001)
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Karl-Heinz Borgwardt
Probabilistic analysis of simplex algorithms
in: Encyclopedia of optimization, ed. by Christodoulos A. Floudas, 368-379 (Kluwer: Dordrecht, 2001)
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Karl-Heinz Borgwardt and Petra Huhn
A lower bound on the average number of Pivot-steps for solving linear programs: valid for all variants of the simplex-algorithm
Mathematical Methods of Operations Research 49, 175-210 (1999)
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Karl-Heinz Borgwardt
A sharp upper bound for the expected number of shadow vertices in LP-polyhedra under orthogonal projection on two-dimensional planes
Mathematics of Operations Research 24, 529-784 (1999)
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Due to an error in typesetting, an incorrect version of Figure 1 was printed as part of this paper in Mathematics of Operations Research, Vol. 24 No. 3, August 1999, pp.

Petra Huhn and Karl-Heinz Borgwardt
An upper bound for the average number of iterations required in phase II of an interior-point-method
Operations Research Proceedings 1997, 19-24 (1998)
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Karl-Heinz Borgwardt
Ideas leading to a better bound on the average number of pivot steps for solving an LP
Operations Research Proceedings 1997, 1-12 (1998)
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Karl-Heinz Borgwardt
Average complexity of a gift-wrapping algorithm for determining the convex hull of randomly given points
Discrete & Computational Geometry 17, 79-109 (1997)
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Auch erschienen als DFG-Schwerpunkt-Report Nr. 478, 1993, 50 Seiten

Karl-Heinz Borgwardt and Jürgen Brzank
Average saving effects in enumerative methods for solving Knapsack problems
Journal of Complexity 10, 129-141 (1994)
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Karl-Heinz Borgwardt
Improving the theoretical upper bound for the expected number of shadow-vertices in the Rotation-Symmetry-Model
(DFG-Schwerpunkt Report ; 537) (1994)
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Karl-Heinz Borgwardt
Versch?rfung des Polynomialit?tsbeweises für die erwartete Anzahl von Schattenecken im Rotationssymmetrie-Modell
in: Beitr?ge zur angewandten Analysis und Informatik : Helmut Brakhage zu Ehren, ed. by Eberhard Schock, (Berichte aus der Mathematik) 13-33 (Shaker: Aachen, 1994)
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auch erschienen als DFG-Schwerpunkt Report Nr. 537, 1994: Improving the Theoretical Upper Bound for the Expected Number of Shadow-Vertices in the Rotation-Symmetry-Model

Karl-Heinz Borgwardt, Renate Damm, Rudolf Donig and Gabriele Joas
Empirical studies on the average efficiency of simplex variants under rotation symmetry
ORSA Journal on Computing 5, 249-260 (1993)
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Karl-Heinz Borgwardt and Gabriele Joas
Verbesserungen in der Laufzeitanalyse des Simplexverfahrens
(Report ; 419) (Universit?t Augsburg, Institut für Mathematik: Augsburg, 1992)
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Karl-Heinz Borgwardt, Norbert Gaffke, Michael Jünger and Gerhard Reinelt
Computing the convex hull in the Euclidean plane in linear expected time
in: Applied geometry and discrete mathematics: the Victor Klee Festschrift, ed. by Bernd Sturmfels and Peter Gritzmann, (DIMACS Series in Discrete Mathematics and Theoretical Computer Science ; 4) 91-107 (American Mathematical Society: Providence, RI, 1991)
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Karl-Heinz Borgwardt and Gabriele Joas
Cycling examples for the shadow vertex algorithm
(Report ; 336) (Universit?t Augsburg, Institut für Mathematik: Augsburg, 1991)
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Karl-Heinz Borgwardt and Birgit Tremel
The average quality of Greedy-algorithms for the subset-sum-maximization problem
Zeitschrift für Operations Research 35, 113-149 (1991)
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Karl-Heinz Borgwardt
Probabilistic analysis of the simplex method
in: Mathematical Developments Arising from Linear Programming, ed. by Jeffrey C. Lagarias and Michael J. Todd, (Contemporary Mathematics ; 114) 1097863 (American Mathematical Society: Providence, Rhode Island, 1990)
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Karl-Heinz Borgwardt
Probabilistic analysis of the simplex method
Operations Research Proceedings 16, 564-575 (1988)
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Karl-Heinz Borgwardt
Probabilistic analysis of optimization algorithms: some aspects from a practical point of view
Acta Applicandae Mathematica 10, 171-210 (1987)
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Karl-Heinz Borgwardt
Probabilistische Analyse von Optimierungs-Algorithmen
Operations research proceedings 15, 571-588 (1987)
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Karl-Heinz Borgwardt
The simplex method: a probabilistic analysis
(Algorithms and Combinatorics ; 1) (Springer: Berlin, 1987)
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Karl-Heinz Borgwardt
Liquidit?tsplanung einer Bank aus mathematischer Sicht
Jahrbuch der Universit?t Augsburg 1985, 171-182 (1986)
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Karl-Heinz Borgwardt
Average behaviour of the simplex-method: some improvements in the analysis of the rotation-symmetry-model
preprint (Universit?t Augsburg, Preprint ; 87) (Universit?t Augsburg: Augsburg, 1985)
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Karl-Heinz Borgwardt
Der durchschnittliche Rechenaufwand beim Simplexverfahren
Operations Research Proceedings 13, 647-660 (1985)
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Karl-Heinz Borgwardt
A probabilistic analysis of the simplex-method [Habilitationsschrift]
(Universit?t Kaiserslautern: Kaiserslautern, 1984)
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Karl-Heinz Borgwardt
Some Distribution-Independent Results About the Asymptotic Order of the Average Number of Pivot Steps of the Simplex Method
Mathematics of Operations Research 7, 441-462 (1982)
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Karl-Heinz Borgwardt
The Average number of pivot steps required by the Simplex-Method is polynomial
Zeitschrift für Operations Research 26, 157-177 (1982)
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Karl-Heinz Borgwardt
Die Problematik rein mathematischer Kriterien für Investitionsentscheidungen
in: Anwendungsorientierter Mathematikunterricht : unter besonderer Berücksichtigung der M?glichkeiten von Rechnern, ed. by Norbert Christmann, 26-36 (Sch?ningh: Paderborn, 1980)
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Karl-Heinz Borgwardt
Die asymptotische Ordnung der mittleren Schrittzahl von Simplexverfahren
Operations-Research-Verfahren = Methods of Operations Research 37, 81-95 (1980)
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Karl-Heinz Borgwardt
Zum Rechenaufwand von Simplexverfahren
Operations-Research-Verfahren = Methods of Operations Research 31, 83-97 (1979)
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Karl-Heinz Borgwardt
Untersuchungen zur Asymptotik der mittleren Schrittzahl von Simplexverfahren in der linearen Optimierung
Operations-Research-Verfahren = Methods of Operations Research 28, 332-345 (1978)
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Karl-Heinz Borgwardt
Untersuchungen zur Asymptotik der mittleren Schrittzahl von Simplexverfahren in der linearen Optimierung
(Universit?t Kaiserslautern: Kaiserslautern, 1977)
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Kaiserslautern, Univ., Diss., 1977