Duality Theory

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 114)


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 we shall study in this chapter.


Dual Problem Linear Programming Problem Duality Theory Simplex Method Primal Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Gale, D., Kuhn, H. & Tucker, A. (1951), Linear programming and the theory of games, in T. Koopmans, ed., ‘Activity Analysis of Production and Allocation’, John Wiley and Sons, New York, pp. 317–329.Google Scholar
  2. Lemke, C. (1954), ‘The dual method of solving the linear programming problem’, Naval Research Logistics Quarterly 1, 36–47.CrossRefMathSciNetGoogle Scholar

Copyright information

© Robert J.Vanderbei 2008

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Dept. of Operations Research and Financial EngineeringPrinceton UniversityNew JerseyUSA

Personalised recommendations