Review by Bob Daniel for Operational Research.

Vanderbei has produced a splendid book. Splendid, but not quite perfect yet, and with small revisions and a rational pricing strategy from the publisher it will be possible to recommend the second edition without reservation.

He deals at a fairly elementary and introductory level with the simplex method, network problems, interior point methods, integer programming, quadratic programming and general convex programming. Along the way there are some detours into convex analysis, elementary game theory, regression and the optimisation of structures.

Implementation issues are covered at a level that would interest the inquisitive reader yet not burden him or her with unnecessary details. For instance sparsity - vital to any practical implementation - is covered very nicely indeed and numerical stability is emphasised.

The section on interior point methods is as beautiful and elegant as one might have hoped from one of the major contributors to the area. It is the best presentation I have seen and it would be very easy to teach an undergraduate course from this book with the expectation that the students would get a lot from the material. Providing of a lot of relevant software on the book's Web site is an added bonus.

The author's wit shines through in the text (quite why he dislikes Newark so much is not clear!) and the selection of examples has been done with great care.

The worked examples are excellent and very much to be welcomed. Resorting to clear examples to demonstrate the theory is usually deprecated - here it is done to great effect.

I have a few quibbles. There are occasional lapses into some mathematical terminology where it is unnecessary. There is one piece of unexplained notation which I and everyone I have shown the book to have never seen before. The coverage of post-optimal analysis is too brief and I think the chapter on optimising structures is slightly self indulgent (but why not?). There is nothing on decomposition.

My major complaint is the price. Kluwer must have no idea what an undergraduate is prepared to spend on a book. Let's have the second edition in paperback at a sensible price please. Then this book will become a classic.