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Book Review

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MathSciNet review: 733260
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Book Information:

Author: Richard W. Cottle
Title: The basic George B. Dantzig
Additional book information: Stanford University Press, Stanford, California, 2003, xvi + 378 pp., ISBN 978-0-8047-4834-6, $57.00, hardcover

References [Enhancements On Off] (What's this?)

  • 1. I. Adler, N. Megiddo, and M. J. Todd.
    New results on the average behavior of simplex algorithms.
    Bulletin of the American Mathematical Society, 11:378-382, 1984. MR 752803 (85h:90074)
  • 2. M. L. Balinski.
    Mathematical programming: Journal, society, recollections.
    In History of Mathematical Programming, (J. K. Lenstra, A. H. G. Rinnooy Kan, and A. Schrijver, editors), Elsevier Science Publishers, 1991, pp. 5-18.
  • 3. A. Ben-Tal and A. Nemirovski.
    Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications.
    MPS-SIAM Series on Optimization. SIAM, Philadelphia, 2001. MR 1857264 (2003b:90002)
  • 4. R. Bixby.
    Solving real-world linear programs: A decade and more of progress.
    Operations Research, 50:3-15, 2002. MR 1885204
  • 5. R. Bland, D. Goldfarb, and M. Todd.
    The ellipsoid method: A survey.
    Operations Research, 29:1039-1091, 1981. MR 641676 (83e:90081)
  • 6. K. H. Borgwardt.
    The Simplex Method: A Probabilistic Analysis.
    Springer-Verlag, Berlin, 1986. MR 868467 (88k:90110)
  • 7. G. B. Dantzig.
    Linear Programming and Extensions.
    Princeton University Press, Princeton, NJ, 1963. MR 0201189 (34:1073)
  • 8. G. B. Dantzig.
    Linear programming.
    In History of Mathematical Programming (J. K. Lenstra, A. H. G. Rinnooy Kan, and A. Schrijver, editors), Elsevier Science Publishers, 1991, pp. 19-31. MR 1183952 (94b:01030)
  • 9. J. Edmonds.
    A glimpse of heaven.
    In History of Mathematical Programming (J. K. Lenstra, A. H. G. Rinnooy Kan, and A. Schrijver, editors), Elsevier Science Publishers, 1991, pp. 32-54. MR 1183952 (94b:01030)
  • 10. J. Faraut and A. Koranyi.
    Analysis on Symmetric Cones.
    Oxford University Press, Oxford, 1994. MR 1446489 (98g:17031)
  • 11. M. Grötschel, L. Lovász, and A. Schrijver.
    Geometric Algorithms and Combinatorial Optimization.
    Springer-Verlag, Berlin, 1988. MR 936633 (89m:90135)
  • 12. B. Grünbaum.
    Convex Polytopes.
    Wiley, New York, 1967. MR 0226496 (37:2085)
  • 13. G. Kalai.
    Linear programming, the simplex algorithm and simple polytopes.
    Mathematical Programming, 79:217-233, 1997. MR 1464768 (98c:90065)
  • 14. G. Kalai and D. J. Kleitman.
    A quasi-polynomial bound for the diameter of graphs of polyhedra.
    Bulletin of the American Mathematical Society, 24:315-316, 1992. MR 1130448 (92h:52017)
  • 15. N. K. Karmarkar.
    A new polynomial-time algorithm for linear programming.
    Combinatorica, 4:373-395, 1984. MR 779900 (86i:90072)
  • 16. L. G. Khachiyan.
    A polynomial algorithm in linear programming (in Russian).
    Doklady Akademiia Nauk SSSR, 224:1093-1096, 1979.
    English Translation: Soviet Mathematics Doklady, 20:191-194, 1979. MR 522052 (80g:90071)
  • 17. L. G. Khachiyan.
    Polynomial algorithms in linear programming (in Russian).
    Zh. Vychisl. Mat. i Mat. Fiz. 20:51-68, 1980.
    English Translation: U.S.S.R. Computational Mathematics and Mathematical Physics, 20:53-72, 1980. MR 564776 (81j:90079)
  • 18. J. Lasserre.
    Moments, Positive Polynomials and Their Applications.
    Imperial College Press, London, 2010.
  • 19. A. S. Nemirovski and M. J. Todd.
    Interior-point methods for optimization.
    Acta Numerica, 17:191-234, 2008. MR 2436012 (2009j:90141)
  • 20. Y. E. Nesterov and A. S. Nemirovski.
    Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms.
    SIAM Publications. SIAM, Philadelphia, USA, 1993.
  • 21. J. Renegar.
    A Mathematical View of Interior-Point Methods in Convex Optimization.
    SIAM, Philadelphia, USA, 2001. MR 1857706 (2002g:90002)
  • 22. A. Schrijver.
    On the history of combinatorial optimization (til 1960).
    In Handbook of Discrete Optimization (K. Aardal, G. Nemhauser, and R. Weismantel, editors), Elsevier Science Publishers, 2005, pp. 1-68.
  • 23. D. Spielman and S.-H. Teng.
    Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time.
    Journal of the ACM, 51:385-463, 2004. MR 2145860 (2006f:90029)
  • 24. D. Spielman and S.-H. Teng.
    Smoothed analysis: An attempt to explain the behavior of algorithms in practice.
    Communications of the ACM, 52:76-84, 2009.
  • 25. M. J. Todd.
    Semidefinite optimization.
    Acta Numerica, 10:515-560, 2001. MR 2009698 (2004g:90004)
  • 26. M. J. Todd.
    The many facets of linear programming.
    Mathematical Programming, 91:417-436, 2002. MR 1888985
  • 27. G. Ziegler.
    Lectures on Polytopes.
    Springer-Verlag, Berlin, 1995. MR 1311028 (96a:52011)

Review Information:

Reviewer: Michael J. Todd
Affiliation: Cornell University
Journal: Bull. Amer. Math. Soc. 48 (2011), 123-129
MSC (2010): Primary 01A60, 65K05, 90-03, 90Cxx
Published electronically: May 19, 2010
Review copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society