Important Peculiarities of the Attic Method

In the following, the starting point is assumed to be feasible, but not necessarily an attic vertex. 

A second important difference in the Attic method is the presence of artificial inequality constraints these are constraints on a single variable and, when they are present in the matrix J, they must be treated differently to the active bound constraints since they are not real constraints. 

A third difference is the exploitation of variables that appear only in one equality or inequality constraint, aside from their bound constraints. If such variables lie on an artificial constraint (that is not an active bound), they allow the equality or 

In an iteration in which the point must be feasible, the following system must be solved  

The iteration continues only if the values of for some artificial constraints are nonzero or if some active inequality constraints have Aj 0 otherwise, the solution is found. Based on the values of k, the elements of a vector h are selected by certain criteria described later and the following linear system is solved  

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