Adding an inequality to a linear program - recovering theorem via Delta of the Duals - Is this an old hat?

2011-10-22T20:15:28Z

Is the theorem below already known?

All inequalities can be transformed to the delta form. $$y_j: (y^0)_j^{-1} \sum_m \Delta^m(y^0_j) s_m \ge \omega(y^0_j) - \omega(y')$$

As an inequality is only defined up to a factor, we can demand $(y^0)_j = 1$. \

This is theorem 7.1 on page 21 of my paper.

The proof is not really difficult, just see everything including the objective function as linear functions and use the two linear representation of the objective.

This little theorem can be used to build a theory of creating new inequalities, when the inequalitiy system has additional properties like integrity for some variables. As it is so easily proved I would assume that it should be known.

For sure the normal method from Mr. Balas is different.

Adding an inequality to a linear program - recovering theorem via Delta of the Duals - Is this an old hat? - MathOverflow

Adding an inequality to a linear program - recovering theorem via Delta of the Duals - Is this an old hat?