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