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To this reviewers knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Methodvia the Ellipsoid algorithm to Karmarkars algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The endofchapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. Mathematics of Computing This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. After preliminary discussion of linear algebra and geometry, it describes the simplex algorithm, duality, the ellipsoid algorithm (Khachiyans algorithm) and Karmarkars algorithm. Zentralblatt Math The exposition is clear and elementary; it also contains many exercises and illustrations. Mathematical Reviews A selfcontained, concise mathematical introduction to the theory of linear programming. Journal of Economic Literature
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