Generalized Linear Programming Solves the Dual

T. L. Magnanti, J. F. Shapiro and M. H. Wagner
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T. L. Magnanti: Massachusetts Institute of Technology
J. F. Shapiro: Massachusetts Institute of Technology
M. H. Wagner: New York University

Management Science, 1976, vol. 22, issue 11, 1195-1203

Abstract: The generalized linear programming algorithm allows an arbitrary mathematical programming minimization problem to be analyzed as a sequence of linear programming approximations. Under fairly general assumptions, it is demonstrated that any limit point of the sequence of optimal linear programming dual prices produced by the algorithm is optimal in a concave maximization problem that is dual to the arbitrary primal problem. This result holds even if the generalized linear programming problem does not solve the primal problem. The result is a consequence of the equivalence that exists between the operations of convexification and dualization of a primal problem. The exact mathematical nature of this equivalence is given.

Date: 1976
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