The Basics

  • Howard Karloff
Part of the Modern Birkhäuser Classics book series (MBC)


Linear Programming is the process of minimizing a linear objective function subject to a finite number of linear equality and inequality constraints. When airlines schedule their crews, when factory managers compute the mix of raw materials which produces the most profitable blend of output products, when utilities plan their oil and gas purchases, they often find themselves setting up and solving problems with hundreds or thousands of variables and constraints. Few problems studied in computer science have greater application in the real world.


Bipartite Graph Inequality Constraint Convex Combination Gaussian Elimination Idealize Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [6]
    A. V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.MATHGoogle Scholar
  2. [9]
    S. Baase, Computer Algorithms: Introduction to Design and Analysis, second edition, Addison-Wesley, Reading, MA, 1988.Google Scholar
  3. [14]
    G. Brassard and P. Bratley, Algorithmics: Theory and Practice, Prentice Hall, Englewood Cliffs, NJ, 1988.MATHGoogle Scholar
  4. [18]
    J. Edmonds, “Systems of Distinct Representatives and Linear Algebra,” Journal of Research of the National Bureau of Standards B 71 (1967), 241-245.MATHMathSciNetGoogle Scholar
  5. [27]
    M. Grotschel, L. Lovasz and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, New York, NY, 1988.Google Scholar
  6. [29]
    I. Herstein, Topics in Algebra, second edition, Wiley, New York, NY, 1975.Google Scholar
  7. [31]
    K. Hoffman and R. Kunze, Linear Algebra, Prentice Hall, Englewood Cliffs, NJ, 1971.MATHGoogle Scholar
  8. [39]
    E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, NY, 1976.MATHGoogle Scholar
  9. [41]
    U. Manber, Introduction to Algorithms: A Creative Approach, Addison-Wesley, Reading, MA, 1989.MATHGoogle Scholar
  10. [44]
    C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall, Engle-wood Cliffs, NJ, 1982.MATHGoogle Scholar
  11. [47]
    A. Schrijver, Theory of Linear and Integer Programming, Wiley, New York, NY, 1986.MATHGoogle Scholar
  12. [56]
    G. Strang, Linear Algebra and Its Applications, third edition, Harcourt Brace Jovanovich, San Diego, CA, 1988.Google Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

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

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