The Theory of Linear Programming

Abstract

In textbooks and papers that consider the theory of linear programming (LP) various techniques are used to prove strong duality and the existence of a strictly complementary solution (Goldman-Tucker’s Theorem [80]). Among others, Balinski and Tucker [14] and Dantzig [39] basically use the simplex method, Farkas Lemma is used by Schrijver [214] and Stoer and Witzgall [222], mathematical induction by Goldman and Tucker [80] and Tucker [234], while Von Neumann and Morgenstern [195] and Rockafellar [207] apply a separation theorem for convex sets. Recently, Güler et al. [96] presented a complete duality theory for LP based on the concepts of interior point methods, making the field of interior point methods for LP self-supporting. Their proofs of the well-known results use almost only analytical arguments.