Research Catalog

Title

The basic George B. Dantzig / edited by Richard W. Cottle.

Author

Dantzig, George B. (George Bernard), 1914-2005

Publication

Stanford, Calif. : Stanford Business Books, 2003.

Items in the Library & Off-site

Details

Additional Authors

Cottle, Richard

Description

xvi, 378 p. : ill., map; 25 cm.

Summary

"George B. Dantzig, widely known as the father of linear programming, has been a major influence in mathematics, operations research, and economics. 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 part of the book 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."--BOOK JACKET.

Uniform Title

Essays. Selections. 2003

Alternative Title

Essays. 2003

Subjects

• Mathematical optimization
• Programming (Mathematics)
• Mathematical statistics
• Dantzig, George B (George Bernard), 1914-2005

Bibliography (note)

• Includes bibliographical references (p. [341]-366) and index.

Contents

I. Mathematical Statistics -- 1. On the nonexistence of tests of "Students" hypothesis having power functions independent of [omega] / George B. Dantzig -- 2. On the fundamental lemma of Neyman and Pearson / George B. Dantzig and Abraham Wald -- II. The Simplex Method of Linear Programming -- 3. Programming in a linear structure / George B. Dantzig -- 4. Maximization of a linear function of variables subject to linear inequalities / George B. Dantzig -- 5. The generalized simplex method for minimizing a linear form under linear inequality restraints / George B. Dantzig, Alex Orden and Philip Wolfe -- III. Large-Scale Linear Programming -- 6. Upper bounds, secondary constraints, and block triangularity in linear programming / George B. Dantzig -- 7. Decomposition principle for linear programs / George B. Dantzig and Philip Wolfe -- 8. Generalized upper bounding techniques / G. B. Dantzig and R. M. Van Slyke -- IV. Special Applications and Economic Modeling -- 9. Minimizing the number of tankers to meet a fixed schedule / G. B. Dantzig and D. R. Fulkerson -- 10. A linear programming approach to the chemical equilibrium problem / G. B. Dantzig, S. Johnson and W. White -- 11. Formulating an objective for an economy / G. B. Dantzig, P. H. McAllister and J. C. Stone -- V. Linear Programming under Uncertainty -- 12. Linear programming under uncertainty / George B. Dantzig -- 13. On the solution of two-stage linear programs under uncertainty / George B. Dantzig and A. Madansky -- 14. Parallel processors for planning under uncertainty / George B. Dantzig and Peter W. Glynn -- 15. Multi-stage stochastic linear programs for portfolio optimization / George B. Dantzig and Gerd Infanger -- VI. Network Optimization -- 16. Solution of a large-scale traveling-salesman problem / G. Dantzig, R. Fulkerson and S. Johnson -- 17. On the max-flow min-cut theorem of networks / George B. Dantzig and D. R. Fulkerson -- 18. On the shortest route through a network / George B. Dantzig -- VII. Integer Linear Programming and Linear Inequalities -- 19. On the significance of solving linear programming problems with some integer variables / George B. Dantzig -- 20. Fourier-Motzkin elimination and its dual / George B. Dantzig and B. Curtis Eaves -- VIII. Nonlinear Programming -- 21. Quadratic programming / George B. Dantzig -- 22. On the continuity of the minimum set of a continuous function / George B. Dantzig, Jon Folkman and Norman Shapiro -- IX. Complementarity Problems -- 23. Complementary pivot theory of mathematical programming / Richard W. Cottle and George B. Dantzig -- 24. A generalization of the linear complementarity problem / Richard W. Cottle and George B. Dantzig.

ISBN

0804748349 (acid-free paper)

LCCN

2003057275

OCLC

• ocm52509658
• SCSB-4829107

Owning Institutions

Columbia University Libraries