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Large Scale Linear and Integer Optimization: A Unified Approach

Large Scale Linear and Integer Optimization: A Unified Approach

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Описание
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 integerlinear 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 audienceis 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.