A simple extension of Fourier-Motzkin elimination is made to mixed systems of equations, that is, systems consisting of equalities in conjunction with inequalities and strict inequalities. The principal observation is that inequalities combined with strict inequalities result in strict inequalities. Two applications are made to automatic data editing. First, a constructive method is provided to test for the existence of a linear objective function for the minimum weighted fields to impute (MWFI) problem with side constraints. If the linear objective function exists, it is determined; if it does not exist, the extension to a quadratic objective function is given. Next, …
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A simple extension of Fourier-Motzkin elimination is made to mixed systems of equations, that is, systems consisting of equalities in conjunction with inequalities and strict inequalities. The principal observation is that inequalities combined with strict inequalities result in strict inequalities. Two applications are made to automatic data editing. First, a constructive method is provided to test for the existence of a linear objective function for the minimum weighted fields to impute (MWFI) problem with side constraints. If the linear objective function exists, it is determined; if it does not exist, the extension to a quadratic objective function is given. Next, for any fixed linear objective function, a solution algorithm based on extended Fourier-Motzkin elimination is given for the resultant MWFI and is illustrated with an example. It is believed that the applications are significant in their own right: they provide solution techniques to difficult problems in the field of automatic data editing.
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