The Basic George B. Dantzig

By: Richard Cottle (Editor)

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Hardcover | 15 September 2003

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398 Pages

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23.39 x 15.6 x 2.54

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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.

Industry Reviews

"George B. Dantzig was one of the most important creative minds of the last half-century. Having a selection of his work is a scholarly must, and anyone interested in the application of quantitative methods to the achievement of efficiency must be grateful." - Kenneth J. Arrow,Nobel Laureate, Stanford University "This collection of papers not only represents a sample of the extraordinary contributions of George Dantzig but also chronicles the fundamental concepts of mathematical programming and operations research. Virtually all of today's work in optimization finds its origin in one or more of these papers. Beyond their historical importance for developing new tools and insights, these articles also demonstrate the elegance and clarity of Dantzig's style of exposition. Students and researchers in all mathematical science fields can learn from his example." - John R. Birge, Dean, Robert R. McCormick School of Engineering and Applied Science, Northwestern University

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Preface	p. ix
Acknowledgments	p. xiii
Mathematical Statistics	p. 1
On the nonexistence of tests of "Students" hypothesis having power functions independent of [sigma]	p. 3
On the fundamental lemma of Neyman and Pearson	p. 10
The Simplex Method of Linear Programming	p. 19
Programming in a linear structure	p. 23
Maximization of a linear function of variables subject to linear inequalities	p. 24
The generalized simplex method for minimizing a linear form under linear inequality restraints	p. 33
Large-Scale Linear Programming	p. 45
Upper bounds, secondary constraints, and block triangularity in linear programming	p. 49
Decomposition principle for linear programs	p. 61
Generalized upper bounding techniques	p. 72
Special Applications and Economic Modeling	p. 89
Minimizing the number of tankers to meet a fixed schedule	p. 91
A linear programming approach to the chemical equilibrium problem	p. 98
Formulating an objective for an economy	p. 105
Linear Programming under Uncertainty	p. 129
Linear programming under uncertainty	p. 131
On the solution of two-stage linear programs under uncertainty	p. 143
Parallel processors for planning under uncertainty	p. 157
Multi-stage stochastic linear programs for portfolio optimization	p. 180
Network Optimization	p. 201
Solution of a large-scale traveling-salesman problem	p. 205
On the max-flow min-cut theorem of networks	p. 225
On the shortest route through a network	p. 232
Integer Linear Programming and Linear Inequalities	p. 237
On the significance of solving linear programming problems with some integer variables	p. 239
Fourier-Motzkin elimination and its dual	p. 255
Nonlinear Programming	p. 265
Quadratic programming	p. 267
On the continuity of the minimum set of a continuous function	p. 276
Complementarity Problems	p. 305
Complementary pivot theory of mathematical programming	p. 307
A generalization of the linear complementarity problem	p. 328
Editor's Notes	p. 341
Publications of George B. Dantzig	p. 353
Index	p. 367
Table of Contents provided by Ingram. All Rights Reserved.

The Basic George B. Dantzig

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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