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Programmation linéaire

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Optimisation combinatoire

Part of the book series: Collection IRIS ((IRIS))

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Résumé

Dans ce chapitre, nous passons en revue les aspects principaux de la programmation linéaire. Bien que se suffisant á elle-même, cette présentation nécessite cependant une connaissance préalable du sujet, que le lecteur non averti pourra trouver dans les livres de référence mentionnés en fin de chapitre.

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Références

Littérature générale

  • Bertsimas, D., Tsitsiklis, J.N. [1997]: Introduction to Linear Optimization. Athena Scientific, Belmont 1997

    Google Scholar 

  • Chvátal, V. [1983]: Linear Programming. Freeman, New York 1983

    MATH  Google Scholar 

  • Matoušek, J., Gärtner, B. [2007]: Understanding and Using Linear Programming. Springer, Berlin 2007

    MATH  Google Scholar 

  • Padberg, M. [1999]: Linear Optimization and Extensions. Second Edition. Springer, Berlin 1999

    MATH  Google Scholar 

  • Schrijver, A. [1986]: Theory of Linear and Integer Programming. Wiley, Chichester 1986

    MATH  Google Scholar 

Références citées

  • Avis, D., Chvátal, V. [1978]: Notes on Bland’s pivoting rule. Mathematical Programming Study 8 (1978), 24–34

    Google Scholar 

  • Bland, R.G. [1977]: New finite pivoting rules for the simplex method. Mathematics of Operations Research 2 (1977), 103–107

    Article  MATH  MathSciNet  Google Scholar 

  • Borgwardt, K.-H. [1982]: The average number of pivot steps required by the simplex method is polynomial. Zeitschrift für Operations Research 26 (1982), 157–177

    Article  MATH  MathSciNet  Google Scholar 

  • Carathéodory, C. [1911]: Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen. Rendiconto del Circolo Matematico di Palermo 32 (1911), 193–217

    Article  MATH  Google Scholar 

  • Dantzig, G.B. [1951]: Maximization of a linear function of variables subject to linear inequalities. In: Activity Analysis of Production and Allocation (T.C. Koopmans, ed.), Wiley, New York 1951, pp. 359–373

    Google Scholar 

  • Dantzig, G.B., Orden, A., Wolfe, P. [1955]: The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific Journal of Mathematics 5 (1955), 183–195

    MATH  MathSciNet  Google Scholar 

  • Farkas, G. [1894]: A Fourier-féle mechanikai elv alkalmazásai. Mathematikai és Természettudom ányi Értesitö 12 (1894), 457–472

    Google Scholar 

  • Gale, D., Kuhn, H.W., Tucker, A.W. [1951]: Linear programming and the theory of games. In: Activity Analysis of Production and Allocation (T.C. Koopmans, ed.), Wiley, New York 1951, pp. 317–329

    Google Scholar 

  • Hoffman, A.J., Kruskal, J.B. [1956]: Integral boundary points of convex polyhedra. In: Linear Inequalities and Related Systems; Annals of Mathematical Study 38 (H.W. Kuhn, A.W. Tucker, eds.), Princeton University Press, Princeton 1956, pp. 223–246

    Google Scholar 

  • Kelner, J.A., Spielman, D.A. [2006]: A randomized polynomial-time simplex algorithm for linear programming. Proceedings of the 38th Annual ACM Symposium on Theory of Computing (2006), 51–60

    Google Scholar 

  • Klee, V., Minty, G.J. [1972]: How good is the simplex algorithm? In: Inequalities III (O. Shisha, ed.), Academic Press, New York 1972, pp. 159–175

    Google Scholar 

  • Kuhn, H.W. [1956]: Solvability and consistency for linear equations and inequalities. The American Mathematical Monthly 63 (1956), 217–232

    Article  MATH  MathSciNet  Google Scholar 

  • Minkowski, H. [1896]: Geometrie der Zahlen. Teubner, Leipzig 1896

    Google Scholar 

  • Motzkin, T.S. [1936]: Beiträge zur Theorie der linearen Ungleichungen (Dissertation). Azriel, Jerusalem 1936

    Google Scholar 

  • von Neumann, J. [1947]: Discussion of a maximum problem. Working paper. Published in: John von Neumann, Collected Works; Vol. VI (A.H. Taub, ed.), Pergamon Press, Oxford 1963, pp. 27–28

    Google Scholar 

  • Spielman, D.A., Teng, S.-H. [2004]: Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. Journal of the ACM 51 (2004), 385–463

    Article  MathSciNet  Google Scholar 

  • Steinitz, E. [1916]: Bedingt konvergente Reihen und konvexe Systeme. Journal für die reine und angewandte Mathematik 146 (1916), 1–52

    Article  Google Scholar 

  • Weyl, H. [1935]: Elementare Theorie der konvexen Polyeder. Commentarii Mathematici Helvetici 7 (1935), 290–306

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Research Institute for Discrete Mathematics, University of Bonn, Lennéstraße 2, 53113, Bonn, Germany

    Bernhard Korte & Jens Vygen

  2. Faculté de mathématiques, Université Paris-VI, 175, rue du Chevaleret, 75013, Paris

    Jean Fonlupt (Professeur émérite)

  3. Panthéon-Sorbonne Centre d’économie de la Sorbonne, Université Paris-I, 106-112, boulevard de l’Hôpital, 75013, Paris

    Alexandre Skoda

Authors
  1. Bernhard Korte
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  2. Jens Vygen
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  3. Jean Fonlupt
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  4. Alexandre Skoda
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Korte, B., Vygen, J., Fonlupt, J., Skoda, A. (2010). Programmation linéaire. In: Optimisation combinatoire. Collection IRIS. Springer, Paris. https://doi.org/10.1007/978-2-287-99037-3_3

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  • DOI: https://doi.org/10.1007/978-2-287-99037-3_3

  • Publisher Name: Springer, Paris

  • Print ISBN: 978-2-287-99036-6

  • Online ISBN: 978-2-287-99037-3

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