Abstract
The purpose of this paper is to prevent some new and unified proofs of a number of known results in combinatorial programming: generalized versions of Minty's lemma, of Ford and Fulkerson's and Hoffman's theorems the length-width inequality and the strong complementary slackness theorem. All these results are derived from a “main duality theorem” which can be deduced from the duality theorem of linear programming or from more general results of convex analysis.
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