Large Scale Linear and Integer Optimization: A Unified Approach (Hardcover)

by Richard Kipp Martin (Author) "This is a textbook about linear and integer linear optimization..." (more)
Key Phrases: degeneracy cone, primal optima, primal path following algorithm, Prove Lemma, Pivot Column Selection, Van Roy (more...)

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. a ] This is an interesting book with special features. a ] 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 Description
Parts I and II of Large Scale Linear and Integer Optimization providean 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 structure by 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.

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.com Sales Rank: #1,809,226 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 1 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

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.