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## Details

Additional Physical Format: | Print version: Dantzig, George Bernard, 1914- Linear programming. v. 2, Theory and Extensions. New York : Springer, 2003 (DLC) 96036411 |
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Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
George Bernard Dantzig; Mukund Narain Thapa |

ISBN: | 9780387215693 0387215697 0387215697 |

OCLC Number: | 424377983 |

Notes: | Titre de l'écran-titre (visionné le 20 mai 2008). |

Description: | 1 online resource. |

Contents: | Cover -- About the authors -- Table of contents -- List of figures -- List of tables -- Preface -- Definition of symbols -- Chapter 1 Geometry of linear inequality systems and the simplex method -- 1.1 Convexity and linear inequality systems -- 1.2 Simplex defined -- 1.3 Global minimum, extreme points, and edges -- 1.4 The simplex method viewed as the steepest descent along edges -- 1.5 The simplex interpretation of the simplex method -- 1.6 Notes & selected bibliography -- 1.7 Problems -- Chapter 2 Duality and theorems of the alternatives -- 2.1 The duality theorem -- 2.2 Additional theorems on duality -- 2.3 Complementary slackness -- 2.4 Theorems of the alternatives -- 2.5 Notes & selected bibliography -- 2.6 Problems -- Chapter 3 Early interior-point methods -- 3.1 Von Neumann's method -- 3.2 Dikin's method -- 3.3 Karmarkar's method -- 3.4 Notes & selected bibliography -- 3.5 Problems -- Chapter 4 Interior-point methods -- 4.1 Newton's method -- 4.2 The linear least-squares problem -- 4.3 Barrier function methods -- 4.4 The primal logarithmic barrier method for solving linear programs -- 4.5 Primal-dual logarithmic barrier methods -- 4.6 Recovering a basic feasible solution -- 4.7 Computational comments -- 4.8 Notes & selected bibliography -- 4.9 Problems -- Chapter 5 Degeneracy -- 5.1 Examples of cycling -- 5.2 On resolving degeneracy -- 5.3 Dantzig's inductive method -- 5.4 Wolfe's rule -- 5.5 Bland's rule -- 5.6 Krishna's extra column rule -- 5.7 On avoiding degenerate pivots -- 5.8 Notes & selected bibliography -- 5.9 Problems -- Chapter 6 Variants of the simplex method -- 6.1 Introduction -- 6.2 Max improvement per iteration -- 6.3 Dual-simplex method -- 6.4 Parametric linear programs -- 6.5 Self-dual parametric algorithm -- 6.6 The primal-dual algorithm -- 6.7 The phase I least-squares algorithm -- 6.8 Notes & selected bibliography -- 6.9 Problems -- Chapter 7 Transportation problem and variations -- 7.1 The classical transportation problem -- 7.2 Finding an initial solution -- 7.3 Finding an improved basic solution -- 7.4 Degeneracy in the transportation problem -- 7.5 Transshipment problem -- 7.6 Transportation problems with bounded partial sums -- 7.7 Notes & selected bibliography -- 7.8 Problems -- Chapter 8 Network flow theory -- 8.1 The maximal flow problem -- 8.2 Shortest route -- 8.3 Minimum cost-flow problem -- 8.4 Notes & selected bibliography -- 8.5 Problems -- Chapter 9 Generalized upper bounds -- 9.1 Problem statement -- 9.2 Basic theory -- 9.3 Solving systems with GUB equations -- 9.4 Updating the basis and working basis -- 9.5 Notes & selected bibliography -- 9.6 Problems -- Chapter 10 Decomposition of large-scale systems -- 10.1 Wolfe's generalized linear program -- 10.2 Dantzig-Wolfe (d-w) decomposition principle -- 10.3 Benders decomposition -- 10.4 Block-angular system -- 10.5 Staircase structured problems -- 10.6 Decomposition used in central planning -- 10.7 Notes & selected bibliography -- 10.8 Problems -- chapter 11 Sto. |

Series Title: | Springer series in operations research. |

Responsibility: | George B. Dantzig, Mukund N. Thapa. |

More information: |

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "This book has a remarkable pair of authors. ... The book contains a large number of examples to illustrate definitions and results. ... While the book is intended as an advanced graduate-level text, I believe that the book, with its wealth of material and detailed examples, is very useful also to upper undergraduate students ... as well as to researchers and practitioners. ... All in all, I think the book is a good value for money for both libraries and individuals." (G Gutin, Journal of the Operational Research Society, Issue 56, 2005) "This book is the second volume of 'Linear Programming' by G.B. Dantzig, and M.N. Thapa ... . The content of the book is about equally split between Linear Programming theory and extensions. ... The book is an essential companion to the first volume ... . As a textbook, the numerous examples and illustrations, especially worked examples of the application of algorithms, are very useful to convey the necessary intuition about the mathematical concepts. ... is also a good reference volume on linear programming." (Matthias Ehrgott, Zentralblatt MATH, Vol. 1029, 2004) "This is Volume 2 of Linear programming ... focussing on the mathematical theory with detailed proofs of all the results. Because of its complete and comprehensive coverage, this volume makes a very attractive textbook for a proof-oriented graduate level course in linear programming (LP). ... It is great having such a comprehensive book on the theory of LP written by the originator of the subject ... . The book belongs in the personal collection of all the people doing research in optimization." (K.G. Murty, Mathematical Reviews, 2004e) "The authors deal with theory and extensions of LP. ... The book contains detailed proofs, worked examples, many exercises and an extensive bibliography, and each chapter is concluded with bibliographical hints and a comprehensive list of problems. This book, coauthored by the originator of the subject, is well-suited as a textbook and a reference on LP." (W. Huyer, Monatshefte fur Mathematik, Vol. 146 (1), 2005) "The book is unique in its integrated treatment ... . The exercises in the book are challenging ... . And the notes at the end of each chapter are especially interesting, because they encapsulate the authors' perspective on and assessment of the current state-of-the-art of linear programming and its extensions." (J.L. Nazareth, SIAM Review, Vol. 46 (3), 2004) "In 1997, 50 years after the invention of the simplex method, Dantzig and Thapa published Linear programming ... . Volume 2, published in 2003, gives a systematic treatment of the theory for readers with a working knowledge of the simplex method and basic linear algebra. ... The book is very carefully and clearly written, with plenty of discussion and commentary on the results and methods, and many worked examples. ... In all respects this is an outstanding advanced text on linear programming." (David Griffel, The Mathematical Gazette, Vol. 88 (513), 2004) "The book is a continuation of Linear Programming 1 ... . The text with full proofs of important theorems and a multitude of exercises invites the reader to actively work on topics ... . each chapter contains a Notes & Selected Biography section which provides the reader with a comprehensive discussion of the scientific literature for further study. The book contains an appendix which provides an overview of probability theory. ... The book ... provides excellent reading materials for a graduate course on the topic." (R. A. Zuidwijk, Kwantitatieve Methoden, 2006) Read more...

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