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Large Scale Linear and Integer Optimization : A Unified Approach - Richard Kipp Martin

Large Scale Linear and Integer Optimization

A Unified Approach


Published: 30th November 1998
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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.

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)

Motivationp. 1
Linear and Integer Linear Optimizationp. 3
Theoryp. 33
Linear Systems and Projectionp. 35
Linear Systems and Inverse Projectionp. 81
Integer Linear Systems: Projection and Inverse Projectionp. 103
Algorithmsp. 141
The Simplex Algorithmp. 143
More on Simplexp. 183
Interior Point Algorithms: Polyhedral Transformationsp. 219
Interior Point Algorithms: Barrier Methodsp. 261
Integer Programmingp. 313
Solving Large Scale Problems: Decomposition Methodsp. 347
Projection: Benders' Decompositionp. 349
Inverse Projection: Dantzig-Wolfe Decompositionp. 369
Lagrangian Methodsp. 393
Solving Large Scale Problems: Using Special Structurep. 437
Sparse Methodsp. 439
Network Flow Linear Programsp. 481
Large Integer Programs: Preprocessing and Cutting Planesp. 527
Large Integer Programs: Projection and Inverse Projectionp. 565
Appendixp. 633
Polyhedral Theoryp. 635
Complexity Theoryp. 657
Basic Graph Theoryp. 677
Software and Test Problemsp. 681
Notationp. 683
Referencesp. 687
Author Indexp. 723
Topic Indexp. 731
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792382027
ISBN-10: 0792382021
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 740
Published: 30th November 1998
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 4.45
Weight (kg): 1.23