Linear Programming

  • Howard Karloff

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages I-X
  2. Howard Karloff
    Pages 1-22
  3. Howard Karloff
    Pages 23-47
  4. Howard Karloff
    Pages 49-71
  5. Howard Karloff
    Pages 73-101
  6. Howard Karloff
    Pages 103-130
  7. Back Matter
    Pages 131-142

About this book


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


Ellipsoid Algorithm Mathematica Rack Simplex Algorithm algorithm algorithms clsmbc complexity complexity theory computational complexity geometry linear algebra linear optimization linear programming programming

Authors and affiliations

  • Howard Karloff
    • 1
  1. 1.College of Computing, Georgia TechAtlantaUSA

Bibliographic information