Customer Reviews

Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6)

5 star:		(14)
4 star:		(3)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

This is an excellent book -- it covers in far more detail the first 2/3rds of the 15.093J/2.098J course at MIT (as well as the more mathematically rigorous 15.081J/6.251J course).
The reader should definitely be a mathematically mature student but even the simplest portable concepts from a linear algebra 101 course (basis, rank of a matrix, linear independence) should suffice.
The authors cover the subject matter first in a geometric sense, but since algorithms are necessarily algebraic, they then present the very same concepts algebraically.
An excellent introductory chapter is followed by chapters on the geometry of LP, the simplex method, duality theory, sensitivity analysis, network flow problems, complexity theory, interior point methods, discrete optimization, IP methods (branch-and-bound, dynamic programming, cutting plane, simulated annealing etc.) and finally, to top it all off and to emphasize and present large, important, real-world problems: the art in linear optimization.
Professor Dimitris Bertsimas is an excellent teacher and he and Professor John Tsitsiklis have excelled themselves at this comprehensive (though, as they state themselves, not encyclopedic) effort.

Prof. Bertsimas and Tsitsiklis succeed in writing a book which is fun to read, without being trivial. It doesn't require much mathematical background (thus being accessible to advanced undergraduates), but present clearly and with sufficient depth relatively new developments like ellipsoid and interior point methods (on the other side, the simplex is given less emphasis than other, older books). Stochastic and integer programming are developed in separate chapters. Another very nice chapter is on "the art of LP". Overall, the book provides the reader with the tools necessary to read the literature in the field. The problems are very well chosen. Unfortunately, the bibliography is not aimed at being complete, but is at least up-to-date

This is an excellent book to learn fundamentals of linear programming and its applications. It's easy to read and it has a great set of of problems, after solving which you'll definitely say that you know something. Among the advantages of the book, I can highlight a great amount of examples, which are easy to follow and very helpful.

There are several minuses of the book. I find it a little wordy, although as I said earlier the writing is very good. Also, the authors try to include as much material as possible, which makes some parts a little superficial. On the other hand the broadness gives the reader a good overview of the field.

Overall, it's a great book for both studies and references.

I think this is an excellent book. The first five chapters develop rigorously the geometry and algebra of linear programming. I studied the book in the context of a class and read almost every word of it. I liked the authors' pace and style -- rigorous, but clear and illuminating. The latter chapters of the book were also good, in particular the integer programming formulations and methods chapters.

The best part of this book is the first half, where the foundations of linear programming are presented in a clear yet relatively rigorous fashion, accompanied by numerous intuitive geometrical explanations of the abstract general concepts. This approach, supplementing mathematics with graphical insights, works extremely well for this topic.

The quality goes down somewhat, perhaps neccessarily, in the latter half of the book as topics are presented less carefully, and in a somewhat rushed manner in order to cover all of the material the authors decided to include. Given that the fundamentals are covered so well, perhaps this is a fair trade.

The only real negative I can think of is that it's a small crime for professors to create their own publishing companies (Athena only publishes works by a small group of MIT professors) and then still charge outrageous amounts for the books. This would be completely unacceptable were it not for the fact that, unlike most self-published work, this book's production quality is on par with that of the large publishers.

If you had to choose only one book on linear programming this is the book. Very well written and up to date. Contrast for example with books that are populated with why? and how? in the text forcing the teacher (or the student) to stop reading and try to solve the question. This book is direct, didactic, and spends 2 pages when the author thinks it is necessary instead of 1 paragraph and 1 why? (to the reader).
The book covers linear programming theory and algorithms, network flows, an introduction to interior point methods and some modeling topics.

This book is THE best LP book I have come across. The topics are very clear and presented in the best possible manner. Introduces you to several basic and advanced LP topics, theorems and algorithms. The exercises at the end of each chapter test the students' understanding in an appropriate manner. A good number of examples are given to explain the theory in a better way. I would definitely recommend this book to a student interested in learning about optimization procedures and/or algorithm development.

Surely helps if you have taken a linear algebra course before. Some students who haven't had a linear algebra course find the math nomenclature formidable in the beginning.

This book is impressive for theory, every thing you ever wanted to know or how to avoid some other is here. I teach to industrial engineering students, so i have to use other books for the application, but for the theory, everything is covered here, even more, in the book are several simple rules to avoid tipical problems of the simplex method or transportation problems, or integer forms. You can't call yourself a pro if you haven't read this book.

This is a great book, good examples and very simple yet precise explanations.
I did like this one! I am studing linear programming at the university and this book helped me a lot, now I understand a lot more than I did with the other books.

This book gives you all the most important aspects about integer programming and linear optimization, you only need basic knowledge in math to understand the proofs and these are explained in an expedited and easy way in order not to lose to the reader. If you do not know much about linear optimization this is the best start and it is solid.