Generalized Linear Programming Solves the Dual
Name
OR-019-73.pdf
Size
1.77 MB
Format
Adobe PDF
Checksum (MD5)
8b15772388cf4ad1d19c2a469a1ad65f
Author(s)
Magnanti, Thomas L.
Shapiro, Jeremy F., 1939-
Wagner, Michael H.
Date Issued
September 1973
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 019-73
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Persistent DSpace Link
