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**Linear programming and network flows.
2nd ed.**
*(English)*
Zbl 0722.90042

New York etc.: John Wiley & Sons. xiv, 684 p. £17.95 (1990).

The book covers both the general theory as well as effective algorithms. Although the first edition appeared already 1977 the new edition can be recommended again for those readers who like to have a profound textbook on these fields which is easy to follow, enriched by a lot of illustrating examples and valuable comments, and is well equipped with plenty exercises covering most of the topics of the book.

The second edition includes detailed geometrically motivated discussions; it covers Karmarkar’s polynomial-time algorithm for linear programming problems and some of its variants. Khachiyan’s ellipsoid algorithm is also sketched, but mainly left to the reader in a well prepared sequence of exercises.

Besides these topics the authors in general tried to update the book to the state-of-the-art while keeping the exposition transparent and easy to follow. One drawback is the merge of the long list of references of the first edition (including only papers which appeared before 1977) and the selected and much shorter list of essential papers, which appeared after that time. In any case the book is full of interesting details and a valuable textbook for advanced undergraduate or first-year graduate students.

The second edition includes detailed geometrically motivated discussions; it covers Karmarkar’s polynomial-time algorithm for linear programming problems and some of its variants. Khachiyan’s ellipsoid algorithm is also sketched, but mainly left to the reader in a well prepared sequence of exercises.

Besides these topics the authors in general tried to update the book to the state-of-the-art while keeping the exposition transparent and easy to follow. One drawback is the merge of the long list of references of the first edition (including only papers which appeared before 1977) and the selected and much shorter list of essential papers, which appeared after that time. In any case the book is full of interesting details and a valuable textbook for advanced undergraduate or first-year graduate students.

Reviewer: H.Noltemeier (Würzburg)