Linear programming (LP) is an area of applied mathematics that is concerned with the minimization (or maximization) of a real-valued linear function on a convex polyhedron. Since the underlying theory is relatively straightforward, the history of the field is dated by the development of algorithms for solving LP problems. Thus the first important contribution was the simplex method developed in 1974 by George Dantzig (4, p. 15). The approach taken by Dantzig was to transform the inequality constraints into a system of equations with sign-restricted variables. This permitted pivoting methods, for solving systems of equations, to be used in linear programming. Thus the simplex method is a set of pivoting rules designed to maximize a linear function constrained by a set of linear equations. Geometrically it can be viewed as an adjacent extreme point method that finds the maximum through an iterative process of implicitly enumerating basic feasible solutions.
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New methods in linear programming
Hatfield, Gordon B.
Follow ACM SIGMAP Bulletin
, Volume (19)
Association for Computing Machinery – Aug 1, 1975
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