American Mathematical Society

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 733260
Full text of review: PDF This review is available free of charge.
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.