Zusammenfassung
Es wird eine ausführliche, anschaulich orientierte Darstellung des Khachiyan Algorithmus' gebracht. Einmal fehlt diese bisher — zumindest im deutschen Sprachraum — soweit ich sehe. Ferner lassen sich so die grundlegenden Ideen des Verfahrens, allgemeine Prinzipien der Algorithmenentwicklung, Vergleiche zur Simplexmethode und Möglichkeiten der Anwendung für andere Probleme als die der Linearen Programmierung recht gut diskutieren.
Abstract
It is given an extended and distinct representation of the Khachiyan algorithm. This fails till now — at least in German-speaking countries — as far as I see. Furthermore basic ideas of the method, general principles of algorithm development, comparisons to the simplex method and possibilities of applications to other problems can be discussed relatively good.
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Literaturverzeichnis
Aspvall, G., undR.E. Stone: Khachiyan's Linear Programming Algorithm. Report STAN-CS-79-776, November 1979, Departments of Computer Science and Operations Research, Stanford University. Stanford 1979.
Berresford, G.C., A.M. Rockett undJ.C. Stevenson: Khachiyan's algorithm I. A new solution to linear Programming problems. BYTE5, 1980, 198–208.
—: Khachiyan's algorithm II. Problems with the algorithm. BYTE5, 1980, 242–255.
Gacs, P., undL. Lovász: Khachian's Algorithm for Linear Programming. Distributed in preliminary form at the X. International Symposium on Mathematical Programming in Montreal, Canada, 27–31 August 1979, and available as Report CS 750, Computer Science Department, Stanford University. Stanford, CA, 1979.
Goldfarb, D., undM.J. Todd: Modifications and Implementation of the Shor-Khachian algorithm for linear programming. Department of Computer Science, Cornell University. Ithaca, N.Y., 1980.
Goldmann, M.: Einige Erläuterungen zum Khachian-Verfahren. ZOR-Zeitschrift für Operations Research25 (4), 1981, B95-B112.
Grötschel, M., L. Lovász undA. Schrijver: The Ellipsoid Method and its Consequences in Combinatorial Optimization. Report No. 80151 - OR, Institut für ökonometrie und Operations Research, Rheinische Friedrich-Wilhelms-Universität Bonn. Bonn 1980.
Khachian, L.G.: A polynomial algorithm in linear programming. Doklady Akademiia Nauk USSR244 (5), 1979, 1093–1096. (Translated at Soviet Mathematics Doklady20, 191–194.)
Kolata, G.B.: Mathematicians Amazed by Russian's Discovery. Science206 (November), 1979, 545–546.
Lawler, E.L.: The Great Mathematical Sputnik of 1979. Time magazine, 1979.
Lovász, L.: A New Linear Programming Algorithm — Better or Worse than the Simplex Method? The mathematical Intelligencer3, 1980, 141–148.
Murray, W.: Ellipsoidal algorithm for linear programming. Working Paper 79-1, Department of Operations Research, Stanford University. Stanford, CA, 1979.
Rosen, J.B., undG. Frawley: A computational test of Khachian's algorithm for linear inequalities. Technical Report 79-28. Computer Science Department, University of Minnesota. Minneapolis, MI, 1979.
Schrader, R.: Ellipsoidal Methods. Modern Applied Mathematics. Optimization and Operations Research. Hrsg. v. B. Korte. Amsterdam-New York-Oxford 1982, 265–311.
Shor, N.Z.: New Development Trends in Nondifferentiable Optimization. Kibernetica13 (1), 1977, 94–96. (Translated at Cybernetics13, 94–96.)
Wolfe, P.: A Bibliography for “Ellipsoidal” Algorithms. IBM Research Center. Yorktown Heights, N.Y., 1980.
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Weber, H.H. Khachiyan's Algorithmus. Zeitschrift für Operations Research 26, B229–B240 (1982). https://doi.org/10.1007/BF01917145
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DOI: https://doi.org/10.1007/BF01917145