Zusammenfassung
Drei Typen von Algorithmen für die LINEARE OPTIMIERUNG hatten die größte Auswirkung, nämlich der SIMPLEXALGORITHMUS (siehe Abschnitt 3.2), die Innere-Punkte-Algorithmen und die ELLIPSOIDMETHODE.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bland, R.G., Goldfarb, D., Todd, M.J.: The ellipsoid method: a survey. Operations Research 29, 1039–1091 (1981)
Edmonds, J.: Systems of distinct representatives and linear algebra. Journal of Research of the National Bureau of Standards B 71, 241–245 (1967)
Frank, A., Tardos, É.: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7, 49–65 (1987)
Gács, P., Lovász, L.: Khachiyan's algorithm for linear programming. Mathematical Programming Study 14, 61–68 (1981)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169–197 (1981)
Iudin, D.B., Nemirovskii, A.S.: Informational complexity and effective methods of solution for convex extremal problems. Ekonomika i Matematicheskie Metody 12, 357–369 (1976) [auf Russisch]
Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica 4, 373–395 (1984)
Karp, R.M., Papadimitriou, C.H.: On linear characterizations of combinatorial optimization problems. SIAM Journal on Computing 11, 620–632 (1982)
Khachiyan, L.G.: A polynomial algorithm in linear programming [auf Russisch]. Doklady Akademii Nauk SSSR 244, 1093–1096 (1979). English translation: Soviet Mathematics Doklady 20, 191–194 (1979)
Khintchine, A.: Kettenbrüche. Teubner, Leipzig (1956)
Padberg, M.W., Rao, M.R.: The Russian method for linear programming III: Bounded integer programming. Research Report 81-39, New York University (1981)
Shor, N.Z.: Cut-off method with space extension in convex programming problems. Cybernetics 13, 94–96 (1977)
Steinitz, E.: Polyeder und Raumeinteilungen. Enzyklopädie der Mathematischen Wissenschaften, Band 3, 1–139 (1922)
Tardos, É.: A strongly polynomial algorithm to solve combinatorial linear programs. Operations Research 34, 250–256 (1986)
Vaidya, P.M.: A new algorithm for minimizing convex functions over convex sets. Mathematical Programming 73, 291–341 (1996)
Weiterführende Literatur
Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin (1988)
Padberg, M.: Linear Optimization and Extensions, 2. Aufl. Springer, Berlin (1999)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Korte, B., Vygen, J. (2012). Algorithmen für lineare Optimierung. In: Kombinatorische Optimierung. Springer-Lehrbuch Masterclass. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25401-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-25401-7_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25400-0
Online ISBN: 978-3-642-25401-7
eBook Packages: Life Science and Basic Disciplines (German Language)