When a Constraint with X 0 Should also be Removed

When a Constraint with X 0 Should also be Removed 

Two additional devices were inserted into the strategy proposed for the Attic method  

The reason behind the first point should be clear if a constraint with Aj 0 is removed, all the constraints subsequently inserted into the matrix are not necessarily roof constraints even though they have A 0 at the working vertex, since their insertions were conditioned by the existing constraints with Aj 0 they are, however, replaced by artificial constraints and therefore the number of iterations to achieve a new vertex does not increase. Conversely, the constraints with a matrix row index smaller than the first constraint removed are reasonably 

In conclusion, there are four devices that can be used to significantly reduce zigzagging problems and cycling between subsets of active constraints in the Attic method  

When variables with no roof constraints exist in the initial point, the best search performed along these axes is selected and compared to the search in the direction providing the maximum improvement of the objective function. 

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