A dual projective simplex method for linear programming

A dual projective simplex method for linear programming

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Article ID: iaor19983014
Country: United Kingdom
Volume: 35
Issue: 6
Start Page Number: 119
End Page Number: 136
Publication Date: Mar 1998
Journal: Computers & Mathematics with Applications
Authors:
Keywords: computational analysis
Abstract:

The method proposed in this paper is a dual version of the projective simplex method, developed by the author. Providing a stable alternative setting for the dual simplex method, by handling a sequence of linear least squares problems using orthogonalization, the method is capable of handling a basis with columns fewer than rows of the coefficient matrix, and amenable to problems with n – m large relative to m, a wide range of problems with which the projective simplex method performs unsatisfactorily, in general. Based on a plausible characterization of an optimal solution, a dual crash heuristic is described to produce an initial ‘good’ basis. Computational results obtained with a set of standard test problems from NETLIB are very encouraging.

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