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An elementary proof of the duality theorem of linear programming

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Abstract

A constructive and elementary proof of the duality theorem of linear programming is presented. The proof utilizes the new concept of an embedded core program, which is a program generated from a linear program with finite optimum by successively removing constraints until no remaining constraints can be deleted without changing the optimal solution.

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References

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    Gale, D., Kuhn, H., andTucker, A.,Linear Programming and the Theory of Games, Activity Analysis of Production and Allocation, Edited by T. C. Koopman, John Wiley and Sons, New York, 1951.

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    Bellman, R., andDreyfus, S.,Applied Dynamic Programming, Appendix II, Princeton University Press, Princeton, New Jersey, 1963.

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    Smith, R. L.,Local Properties of the Resource-Return Function of Linear and Convex Programming, University of California at Berkeley, Operations Research Center, Report No. 71–8, 1971.

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Communicated by S. E. Dreyfus

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Smith, R.L. An elementary proof of the duality theorem of linear programming. J Optim Theory Appl 12, 129–135 (1973). https://doi.org/10.1007/BF00934813

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Keywords

  • Duality Theorem
  • Elementary Proof
  • Core Program
  • Complementary Slackness
  • Unique Optimal Solution