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Duality and Complementarity

In: Linear and Nonlinear Programming

Author

Listed:
  • David G. Luenberger

    (Stanford University)

  • Yinyu Ye

    (Stanford University)

Abstract

Associated with every linear program, and intimately related to it, is a corresponding dual linear program. Both programs are constructed from the same underlying cost and constraint coefficients but in such a way that if one of these problems is one of minimization the other is one of maximization, and the optimal values of the corresponding objective functions, if finite, are equal. The variables of the dual problem can be interpreted as prices associated with the constraints of the original (primal) problem, and through this association it is possible to give an economically meaningful characterization to the dual whenever there is such a characterization for the primal.

Suggested Citation

  • David G. Luenberger & Yinyu Ye, 2016. "Duality and Complementarity," International Series in Operations Research & Management Science, in: Linear and Nonlinear Programming, edition 4, chapter 0, pages 83-114, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-18842-3_4
    DOI: 10.1007/978-3-319-18842-3_4
    as

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