Linear Programming 2: Theory and Extensions

ISBN-13: 9780387986135 / Angielski / Twarda / 2003 / 448 str.

George B. Dantzig; Mukund N. Thapa

Opis

Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering, and applied mathematics will find this volume of particular interest.

Recenzje

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 für 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)

Spis treści

Geometry of Linear Inequality Systems and the Simplex Method * Duality and Theorems of the Alternatives * Early Interior-Point Methods * Interior-Point Methods * Degeneracy * Variants of the Simplex Method * Transportation Problem and Variations * Network Flow Theory * Generalized Upper Bounds * Decomposition of Large-Scale Systems * Stochastic Programming: Introduction * Two-Stage Stochastic Programs * Appendix: Probability Theory: Overview