Customer Reviews

Linear Programming (Series of Books in the Mathematical Sciences)

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

 

 

I've been teaching a linear programming course at the advanced undergraduate level out of this book for the last 12 years. I'm still happy with Chvatal's book and haven't found anything better.

Prerequisites for this book include some background in linear algebra (the typical sophomore level introduction to linear algebra is enough), and some experience with proof based mathematics. Because the subject does not involve the difficult concepts of analysis, it (much like number theory) makes a good subject for students to study as they are developing proof writing skills.

The first 10 chapters of the book present the simplex method, the revised simplex method, duality theory, and sensitivity analysis.
This material can easily be covered in 10 weeks. The remaining chapters of the book are largely independent, mostly focused on various applications of linear programming and specialization of the simplex method to network flow problems.

Chvatal presents the simplex method and many of its applications from a mathematical point of view. He states and proves theorems, but also provides plenty of motivation. Students who make an effort do develop more mathematical maturity from working through this book.

Chvatal also presents the material from a computational and algorithmic point of view. One of the major points of the book is that the author prefers to use algorithmic proofs. For example, the proof that every standard form LP is either infeasibile, unbounded, or has an optimal BFS is built on the simplex method- Since the algorithm terminates in one of these three states, and can't go into an infinite loop, these are the only possibilities.

Another particular strength of the book is in the presentation of duality theory. The explanation is simply very clear and intuitive.

The one glaring weakness of the book is that it doesn't contain any discussion of interior point methods for linear programming. Since the book was published in the mid 1980's, this is not surprising. In my course, I supplement Chvatal's book with my own lecture notes on interior point methods.

This book is a good introduction to linear programming. And very readable. It also serves as a good reference. For a more advanced text and non-linear programming topics, look at Nash and Sofer.

I had such a hard time following up with this book. There is no complete examples. The book explains the initial and final steps to problems skipping many important details in the middle. The example problem in chapter 8 about the bounded revised simplex method took me 5 days to understand. Also, the complametary slackness example in chapter 5 was confusing to understand.

As a student, I wouldn't recommend this book to anyone trying to learn linear programming for the first time.

I cut my teeth on this text in George Nemhauser's class. The book is clear and concise and does an excellent job explaining this topic to beginners. I've not come across a better introductory text yet. I still have this book in my reference library.

If you want an introduction to LP, this is the text for you.

The book is concise and easy to read, but the explanation is not very clear. Still, the book lacks of examples and exercises, and even selected ones didn't provide clear answers.

Honestly, I had studied some other LP and Linear Algebra books before I came across this book; otherwise, I wouldn't have understood it.

A masterpiece on Linear Programming. Although it does not contain Interior Point Methods developed subsequently, it's always the first book I refer to, whenever I have any questions on Linear Programming. Strongly Recommended.

The book presents many aspects of linear programming, particularly basic concepts, in a much simpler and interesting way than earlier books on this area. If focuses on what I consider the relevant aspects of LP and avoids sections describing endless calculations. Besides basic and some advanced concepts, there is an entire section devoted to applications which is interesting for engineering courses.

The book offers an objective treatment of linear programming, in small self contained chapters. I consider this title the best introdutory text on LP, just because it is extremely well written. The major drawback of this book is the small and easy number of exercises proposed at the end of the chapters. The text is not an updated book on the subject, but I really recomend it.

i don't understand why everyone is giving this book such great reviews. as a linear programming student, i find this book extremely difficult to understand, very poorly orgranized, extremely lacking in practical examples to demonstrate the concepts that the author is attempting to describe, and basically a piece of garbage. it was obviously written by a mathematician, not someone capable of teaching. i would not recommend it to anyone.