The Basic George B. Dantzig

by Cottle, Richard

• ISBN13: 9780804748346
• ISBN10: 0804748349
• Format: Hardcover
• Copyright: 2003-10-01
• Publisher: Stanford Business Books

Summary

The late George B. Dantzig , widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings.

Author Biography

Richard W. Cottle is Professor of Management Science and Engineering at Stanford University.

Table of Contents

Preface	ix
Acknowledgments	xiii
I. Mathematical Statistics	1	(18)
1. On the nonexistence of tests of "Students" hypothesis having power functions independent of σ
GEORGE B. DANTZIG	3	(7)
2. On the fundamental lemma of Neyman and Pearson
GEORGE B. DANTZIG AND ABRAHAM WALD	10	(9)
II. The Simplex Method of Linear Programming	19	(26)
3. Programming in a linear structure
GEORGE B. DANTZIG	23	(1)
4. Maximization of a linear function of variables subject to linear inequalities
GEORGE B. DANTZIG	24	(9)
5. The generalized simplex method for minimizing a linear form under linear inequality restraints
GEORGE B. DANTZIG, ALEX ORDEN, AND PHILIP WOLFS	33	(12)
III. Large-Scale Linear Programming	45	(44)
6. Upper bounds, secondary constraints, and block triangularity in linear programming
GEORGE B. DANTZIG	49	(12)
7. Decomposition principle for linear programs
GEORGE B. DANTZIG AND PHILIP WOLFS	61	(11)
8. Generalized upper bounding techniques
G.B. DANTZIG AND R.M. VAN SLYKE	72	(17)
IV. Special Applications and Economic Modeling	89	(40)
9. Minimizing the number of tankers to meet a fixed schedule
G.B. DANTZIG AND D.R. FULKERSON	91	(7)
10. A linear programming approach to the chemical equilibrium problem
G.B. DANTZIG, S. JOHNSON, AND W. WHITE	98	(7)
11. Formulating an objective for an economy
G.B. DANTZIG, P.H. MC ALLISTER, AND J.C. STONE	105	(24)
V. Linear Programming under Uncertainty	129	(72)
12. Linear programming under uncertainty
GEORGE B. DANTZIG	131	(12)
13. On the solution of two-stage linear programs under uncertainty
GEORGE B. DANTZIG AND A. MADANSKY	143	(14)
14. Parallel processors for planning under uncertainty
GEORGE B. DANTZIG AND PETER W. GLYNN	157	(23)
15. Multi-stage stochastic linear programs for portfolio optimization
GEORGE B. DANTZIG AND GERD INFANGER	180	(21)
VI. Network Optimization	201	(36)
16. Solution of a large-scale traveling-salesman problem
G. DANTZIG, R. FULKERSON, AND S. JOHNSON	205	(20)
17. On the max-flow min-cut theorem of networks
GEORGE B. DANTZIG AND D.R. FULKERSON	225	(7)
18. On the shortest route through a network
GEORGE B. DANTZIG	232	(5)
VII. Integer Linear Programming and Linear Inequalities	237	(28)
19. On the significance of solving linear programming problems with some integer variables
GEORGE B. DANTZIG	239	(16)
20. Fourier-Motzkin elimination and its dual
GEORGE B. DANTZIG AND B. CURTIS EAVES	255	(10)
VIII. Nonlinear Programming	265	(40)
21. Quadratic programming
GEORGE B. DANTZIG	267	(9)
22. On the continuity of the minimum set of a continuous function
GEORGE B. DANTZIG, JON FOLKMAN, AND NORMAN SHAPIRO	276	(29)
IX. Complementarity Problems	305	(36)
23. Complementary pivot theory of mathematical programming
RICHARD W. COTTLE AND GEORGE B. DANTZIG	307	(34)
24. A generalization of the linear complementarity problem
RICHARD W. COTTLE AND GEORGE B. DANTZIG 32$
Editor's Notes	341	(12)
Publications of George B. Dantzig	353	(14)
Index	367