Book Review
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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
- 1. Ilan Adler, Nimrod Megiddo, and Michael J. Todd, New results on the average behavior of simplex algorithms, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 378–382. MR 752803, https://doi.org/10.1090/S0273-0979-1984-15317-5
- 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. Aharon Ben-Tal and Arkadi Nemirovski, Lectures on modern convex optimization, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Programming Society (MPS), Philadelphia, PA, 2001. Analysis, algorithms, and engineering applications. MR 1857264
- 4. Robert E. Bixby, Solving real-world linear programs: a decade and more of progress, Oper. Res. 50 (2002), no. 1, 3–15. 50th anniversary issue of Operations Research. MR 1885204, https://doi.org/10.1287/opre.50.1.3.17780
- 5. Robert G. Bland, Donald Goldfarb, and Michael J. Todd, The ellipsoid method: a survey, Oper. Res. 29 (1981), no. 6, 1039–1091. MR 641676, https://doi.org/10.1287/opre.29.6.1039
- 6. Karl-Heinz Borgwardt, The simplex method, Algorithms and Combinatorics: Study and Research Texts, vol. 1, Springer-Verlag, Berlin, 1987. A probabilistic analysis. MR 868467
- 7. George B. Dantzig, Linear programming and extensions, Princeton University Press, Princeton, N.J., 1963. MR 0201189
- 8. Jan Karel Lenstra, Alexander H. G. Rinnooy Kan, and Alexander Schrijver (eds.), History of mathematical programming, North-Holland Publishing Co., Amsterdam; Centrum voor Wiskunde en Informatica, Amsterdam, 1991. A collection of personal reminiscences. MR 1183952
- 9. Jan Karel Lenstra, Alexander H. G. Rinnooy Kan, and Alexander Schrijver (eds.), History of mathematical programming, North-Holland Publishing Co., Amsterdam; Centrum voor Wiskunde en Informatica, Amsterdam, 1991. A collection of personal reminiscences. MR 1183952
- 10. Jacques Faraut and Adam Korányi, Analysis on symmetric cones, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1446489
- 11. Martin Grötschel, László Lovász, and Alexander Schrijver, Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics: Study and Research Texts, vol. 2, Springer-Verlag, Berlin, 1988. MR 936633
- 12. Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. MR 0226496
- 13. Gil Kalai, Linear programming, the simplex algorithm and simple polytopes, Math. Programming 79 (1997), no. 1-3, Ser. B, 217–233. Lectures on mathematical programming (ismp97) (Lausanne, 1997). MR 1464768, https://doi.org/10.1016/S0025-5610(97)00061-0
- 14. Gil Kalai and Daniel J. Kleitman, A quasi-polynomial bound for the diameter of graphs of polyhedra, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 2, 315–316. MR 1130448, https://doi.org/10.1090/S0273-0979-1992-00285-9
- 15. N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), no. 4, 373–395. MR 779900, https://doi.org/10.1007/BF02579150
- 16. L. G. Hačijan, A polynomial algorithm in linear programming, Dokl. Akad. Nauk SSSR 244 (1979), no. 5, 1093–1096 (Russian). MR 522052
- 17. L. G. Hačijan, Polynomial algorithms in linear programming, Zh. Vychisl. Mat. i Mat. Fiz. 20 (1980), no. 1, 51–68, 260 (Russian). MR 564776
- 18.
J. Lasserre.
Moments, Positive Polynomials and Their Applications.
Imperial College Press, London, 2010. - 19. Arkadi S. Nemirovski and Michael J. Todd, Interior-point methods for optimization, Acta Numer. 17 (2008), 191–234. MR 2436012, https://doi.org/10.1017/S0962492906370018
- 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. James Renegar, A mathematical view of interior-point methods in convex optimization, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Programming Society (MPS), Philadelphia, PA, 2001. MR 1857706
- 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. Daniel A. Spielman and Shang-Hua Teng, Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time, J. ACM 51 (2004), no. 3, 385–463. MR 2145860, https://doi.org/10.1145/990308.990310
- 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 Numer. 10 (2001), 515–560. MR 2009698, https://doi.org/10.1017/S0962492901000071
- 26. Michael J. Todd, The many facets of linear programming, Math. Program. 91 (2002), no. 3, Ser. B, 417–436. ISMP 2000, Part 1 (Atlanta, GA). MR 1888985, https://doi.org/10.1007/s101070100261
- 27. Günter M. Ziegler, Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995. MR 1311028
Review Information:
Reviewer: Michael J. Todd
Affiliation: Cornell University
Email: mjt7@cornell.edu
Journal: Bull. Amer. Math. Soc. 48 (2011), 123-129
MSC (2010): Primary 01A60, 65K05, 90-03, 90Cxx
DOI: https://doi.org/10.1090/S0273-0979-2010-01303-3
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.