Large Scale Linear and Integer Optimization: A Unified Approach [Hardcover]

Richard Kipp Martin (Author)

Book Description

Publication Date: November 30, 1998 | ISBN-10: 0792382021 | ISBN-13: 978-0792382027 | Edition: 1

There is a growing need in major industries such as airline, trucking, financial engineering, etc. to solve very large linear and integer linear optimization problems. Because of the dramatic increase in computing power, it is now possible to solve these problems. Along with the increase in computer power, the mathematical programming community has developed better and more powerful algorithms to solve very large problems. These algorithms are of interest to many researchers in the areas of operations research/management science, computer science, and engineering. In this book, Kipp Martin has systematically provided users with a unified treatment of the algorithms and the implementation of the algorithms that are important in solving large problems. Parts I and II of Large Scale Linear and Integer Programming provide an introduction to linear optimization using two simple but unifying ideas-projection and inverse projection. The ideas of projection and inverse projection are also extended to integer linear optimization. With the projection-inverse projection approach, theoretical results in integer linear optimization become much more analogous to their linear optimization counterparts. Hence, with an understanding of these two concepts, the reader is equipped to understand fundamental theorems in an intuitive way. Part III presents the most important algorithms that are used in commercial software for solving real-world problems. Part IV shows how to take advantage of the special structure in very large scale applications through decomposition. Part V describes how to take advantage of special structureby modifying and enhancing the algorithms developed in Part III. This section contains a discussion of the current research in linear and integer linear programming. The author also shows in Part V how to take different problem formulations and appropriately `modify' them so that the algorithms from Part III are more efficient. Again, the projection and inverse projection concepts are used in Part V to present the current research in linear and integer linear optimization in a very unified way. While the book is written for a mathematically mature audience, no prior knowledge of linear or integer linear optimization is assumed. The audience is upper-level undergraduate students and graduate students in computer science, applied mathematics, industrial engineering and operations research/management science. Course work in linear algebra and analysis is sufficient background.

Editorial Reviews

Review

From the reviews of the first edition: "This book is a very comprehensive textbook of linear and integer optimization. It presents a unified approach to the subject and is one of the few books treating linear and integer aspects together. … This is an interesting book with special features. … The text is written in a clear and readily comprehensible way, and it contains computer programs as well as many examples being helpful for students. This book is an important textbook of mathematical programming." (Johannes Jahn, Zentralblatt MATH, Vol. 1053 (4), 2005)

Product Details

• Hardcover: 764 pages
• Publisher: Springer; 1 edition (November 30, 1998)
• Language: English
• ISBN-10: 0792382021
• ISBN-13: 978-0792382027
• Product Dimensions: 9.6 x 6.3 x 1.9 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,252,499 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

1 of 2 people found the following review helpful:

5.0 out of 5 stars Original and highly intuitive contribution to the field, November 10, 2000

By 

Peter Cacioppi - Sr. Software Developer Logic... (Eugene, OR USA) - See all my reviews

This review is from: Large Scale Linear and Integer Optimization: A Unified Approach (Hardcover)

The concepts of projection and inverse projection represent a highly original and intuitive contribution to the study of linear and mixed integer programming. These ideas allow Prof. Martin to explore a challenging subject in a manner that is clear and easy to understand. This text is usefull both to the novice looking for an introduction to mathematical optimzation and to the expert interested in exploring a novel approach to the field.

I was especially impressed with the material on how degeneracy can be handled with the Simplex method. The book presents a fascinating twist on Bland's classic row selection rule.