To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method...via the Ellipsoid algorithm to Karmarkar’s 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 end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study.
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 (Khachiyan’s algorithm) and Karmarkar’s algorithm.
The exposition is clear and elementary; it also contains many exercises and illustrations.
A self-contained, concise mathematical introduction to the theory of linear programming.
—Journal of Economic Literature