Linear Programming pp 55-87 | Cite as

# Duality Theory

Chapter

## Abstract

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.

## Keywords

Dual Problem Linear Programming Problem Duality Theory Simplex Method Primal Problem
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## References

- 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 - 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