Synopses & Reviews
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.
-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 (Khachiyan's algorithm) and Karmarkar's algorithm.
-Zentralblatt Math
The exposition is clear and elementary; it also contains many exercises and illustrations.
-Mathematical Reviews
A self-contained, concise mathematical introduction to the theory of linear programming.
-Journal of Economic Literature
Synopsis
Linear Programming is a concise, thorough, mathematical introduction to the theory of linear programming, viewed as a study of algorithms. Requiring nothing more than basic linear algebra for comprehension, it presents rigorous and lucid expositions of such topics as the simplex algorithm, the ellipsoid algorithm, and Karmarkara (TM)s algorithm. It provides for the practitioner a blend of rigor, intuition, and motivation for understanding the theory and applying it to such topics as game theory and algorithm design.
A distinctive feature of the book is a detailed proof of the polynomiality of running time for Karmarkara (TM)s algorithm and ellipsoid algorithm. Another is its computer science prospective which addresses the issue of computational complexity with great care.
Practitioners, advanced undergraduate and graduate students in mathematics, computer science, operations research, and numerical analysis will find this book a mathematically satisfying exposition of linear programming. They will also find it an accessible adjunction to and application of a course in linear algebra.