Average Reviews:
(More customer reviews)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.
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For upper-division/graduate courses in operations research/management science, mathematics, and computer science, this text covers basic theory, selected applications, network flow problems, and advanced techniques.
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