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Dear all, which book about Linear Programming do you consider the definitive reference at the moment? I liked the book by Vanderbei very much as a tutorial-like introduction to the topic. Now I'm searching for a more comprehensive book. Edit: Thanks for your suggestions so far. Finally, I had two candidates: the book by Luenberger and Ye and the book by Bertsimas and Tsitsiklis. I decided to buy the former, since it covers a slightly broader spectrum (as judged from the toc). Furthermore I have read the Papadimitrou/Steiglitz, which is excellent but mainly concerned with integer programming. |
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I think Linear Programming from professor Chvatal covers all important topic about LP. That's a pretty dated reference. It was excellent 10-20 years ago--and is still good for an undergraduate audience--but leaves something to be desired now. For example, it doesn't talk about using LP for approximating (via integer programming), stochastic programming problems, interior point methods, or other modern large-scale algorithms.
(Jan 23 '12 at 03:44)
Chris Jordan Squire
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The course on linear programming in my undergraduate program used: Introduction to Operations Research by Hiller and Lieberman but it does discuss a number of topics that are not exclusively LP since the book is a reference for Operations Research. I'd still encourage looking at it I find it useful. Karloff's book and Kolman/Beck's book would be reasonable as well. Then again the LP book I've had on my bookshelf the longest is Papadimitriou's Combinatorial Optimization: Algorithms and Complexity I've learned a lot from this one on my own time. Generally speaking though a book that addresses a wide variety of topics tends to sacrifice a degree of detail (more breadth than depth) so more comprehensive coverage (more depth than breadth) would have to come from more specialized texts (or perhaps journal articles) on a particular topic. You might consider looking at the books and papers your book cites and see if they provide the greater coverage you're seeking. |
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My personal favorite reference for basic linear optimization methods and applications is Introduction to Linear Optimization by Bertsimas and Tsitsiklis. It's quite comprehensive, and is targeted for a graduate audience that's already familiar with linear algebra. I agree with Chris Simokat that most of the books cover similar material. If you want something not covered in Vanderbei then going directly to the more specialized literature is probably the next step. |
I was just taught a course with http://www.amazon.com/Introduction-Linear-Optimization-Scientific-Computation/dp/1886529191
It's by Bertsimas and Tsitsiklis, and is quite extensive.