Wonderful book
I used this book for TAing my undergrad and grad classes. It is an unbeatable book in Linear Programming. The authors developed not only a strong linear algebric concept but also a wonderful geometric concept of LPs. By the way, it is not a beginner's book. I suggest Winston's book for the beginners.
Very Theoretical but good fundamental and advanced techniques
The techniques described are very theoretical but are friendly to be used in Computer programs. Has a great deal of depth.
This book is only useful if you already know about linear programming.
I am using this book for a linear programming course. The most flagrant problem with this book is that it is filled with typos, making reading through proofs and examples very frustrating because you're never sure what is supposed to be written. The book is also not very good at explaining concepts and leaves many steps out in the development of new ideas. If you can avoid it, do not use this book to learn linear programming.
It Could be better
In my point of view this book has 2 related problems:
Problem 1. It tries to pack much information in a small space.
Problem 2. I dont like the author's style of asking why? and how? to the reader in the midst of the text. Maybe this is to keep the book small but it forces you to stop reading and think about the question.
However, I think this book is a good reference. But, certainly the authors could have made it better. Let's wait for the next edition.
Strong Graduate Treatment in Linear Programming
I used this text while taking a graduate linear programming (LP)course on LP and network flows. I really liked the treatment. The typesetting was clear ,consistent and easily followed (not as good as Nash and Sofer's). The book also includes lots of nice side discussion on how or why the theory is the way it is. Plenty of references are offered for further study. Proofs were not rigorous. The highly mathematical reader may be disappointed by the "show proof" style used instead of a rigorous theorem-proof style. In fact, I seem to recall a time or two where the theorem came after the usage. For me, I didn't mind that, but a pure math guy would likely grind his teeth.The network material was acceptable. I personally thought the text problems were not of the best quality. I would suggest a teacher supplement their own favorites outside of the book.
One caution is that the book is somewhat aged. I noticed a text like Nash and Sofer seems to have newer updates on the theory.
Overall, a great read for getting into the nitty gritty details of LP.
