Duality Theory

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 196)


Associated with every linear program is another called its dual. The dual of this dual linear program is the original linear program (which is then referred to as the primal linear program). Hence, linear programs come in primal/dual pairs. It turns out that every feasible solution for one of these two linear programs gives a bound on the optimal objective function value for the other. These ideas are important and form a subject called duality theory, which is the topic of this chapter.


  1. Gale, D., Kuhn, H., and Tucker, A. (1951). Linear programming and the theory of games. In T. Koopmans (Ed.), Activity analysis of production and allocation (pp. 317–329). New York: Wiley.Google Scholar
  2. Lemke, C. (1954). The dual method of solving the linear programming problem. Naval Research Logistics Quarterly, 1, 36–47.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

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