Linear Programs & Related Problems: A Volume in the COMPUTER SCIENCE and SCIENTIFIC COMPUTING Series [Hardcover]

Evar D. Nering (Author), Albert W. Tucker (Author)

Book Description

Publication Date: October 26, 1992 | ISBN-10: 0125154402 | ISBN-13: 978-0125154406 | Edition: 1

This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.

Editorial Reviews

From the Back Cover

This text is concerned with the theory of linear and nonlinear programming, related problems, and the algorithms appropriate to the problems. The concept of duality is introduced early and serves as a unifying theme throughout the book. It is used to provide insight, interpret results, and provide practical information.

In this book the maximization problem and its dual minimization problem are considered together, and solving either problem automatically provides a solution to the other. The related topics in matrix games, assignment problems, transportation problems, network-flow problems, and transshipment problems are also treated simultaneously with their dual problems.

The tableaux are used as graphical tools to assist the reader in determining what the next step should be, whether the problem is feasible, whether it has an optimal solution, and , if it does, solutions to both of the dual problems at the same time.

The answer set is extensive. It includes the correct result for all of the problems in the text and, for many problems, a thorough explanation of how to arrive at that result. There is also an IBM compatible disk accompanying the text that includes programs for doing the arithmetic work associated with pivoting in tableaux and the Hungarian algorithm. The data files for the appropriate exercises are included, and new data can be entered and saved. User-selected results may be printed

About the Author

Evar D. Nering received his Ph.D. at Princeton University under the direction of Emil Artin. His early publications were in algebraic number theory and game theory. He was the author of two books on linear algebra, Linear Algebra and matrix Theory (John Wiley & Sons, 1963, 1970) and Elementary Linear Algebra (Saunders, 1973).His most recent activity has been in mathematical programming, including his collaboration with Albert W. Tucker since 1973. He was a faculty member at the University of Minnesota, The University of Arizona, and Arizona State University until his retirement in 1990. At Arizona State University he was Chairman of the Mathematics Department and a consultant to the faculty and staff on microcomputers.

The career of Albert W. Tucker spans more than 50 years at Princeton University. Best known today for his work in mathematical programming and game theory (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner's Dilemma), he was also prominent in combinational topology in his earlier years. An outstanding teacher, leader, and editor, he has been Chairman of the Princeton Mathematics Department, President of the MAA, Chairman of the Mathematical Programming Society, and course instructor, thesis advisor, or general mentor to scores of active mathematicians. For many years before his retirement in 1974, he taught a popular junior-senior course in games and programs, the notes for which grew into this book-thanks to Evar D. Nering.

Product Details

• Hardcover: 584 pages
• Publisher: Academic Press; 1 edition (October 26, 1992)
• Language: English
• ISBN-10: 0125154402
• ISBN-13: 978-0125154406
• Product Dimensions: 8.9 x 5.9 x 1.4 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,580,476 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

4.0 out of 5 stars Karmarkar and back again, June 22, 2000

By A Customer

This review is from: Linear Programs & Related Problems: A Volume in the COMPUTER SCIENCE and SCIENTIFIC COMPUTING Series (Hardcover)

Don't read this book expecting computer programming instruction in the "linear" language. It's a whole different animal of operations research. Linear programming concerns minimizing and maximizing linear functions under a set of linear constraints. This book brings the best problems to linear programming solves and the recent theorems. I found it's handling of the Karmarkar algorithm easier to follow than most other I've seen. It's hard to find information this current outside of journals.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Karmarkar and back again, June 22, 2000

By A Customer

This review is from: Linear Programs & Related Problems: A Volume in the COMPUTER SCIENCE and SCIENTIFIC COMPUTING Series (Hardcover)

As an undergrad math major, I found this book incredibly helpful in understanding the Karmarker Algorithm or, more specifically, their twist on it. Some sections require many rereadings and the differences between their explanations and the original Karmarkar article are stark. But, overall, it's a clear a read as can be expected from an math/operations research text.