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Published in:
2016 | OriginalPaper | Chapter
Theorems of Linear Programming
Author : Quirino Paris
Published in: An Economic Interpretation of Linear Programming
Publisher: Palgrave Macmillan US
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The material of this chapter is taken from papers of D. Gale, A. W. Tucker, A. J. Goldman, H. W. Kuhn and G. B. Dantzig. The scope of this chapter is to provide a concise presentation of the principal theorems that justify the structure of linear programming and the development of the simplex algorithms. The theorem (lemma) by Hungarian mathematician Julius Farkas, presented in 1894 and again in 1902, is of fundamental importance for establishing the structure of a dual pair of LP problems. An imaginative and operational lemma to prove Farkas theorem is due to A. W. Tucker. The statement of standard and canonical LP problems follows the structure presented by D. Gale.