Equality Gauss factorization

Lastly, it is also possible to use the method that exploits the null space of the constraints. Once again in this case, all the active bounds must first be removed from the problem. Only then it is possible to use either LQ factorization or a stable Gauss factorization of all the equality and active inequality constraints. This gives the KKT conditions for an unconstrained problem, as has already been demonstrated for equality constraints. 

Let us do some substitutions here. Assuming a typical current density of 600 cmil/A, utilization factor K of 0.3, AB equal to 1500 gauss, we get the following fundamental core-selection criterion ... 

In developing the first item, the fact that, according to Gauss equation H8.2, the divergence of the electric field is proportional to the charge concentration has been taken into account, so its gradient is zero because the charge concentration is supposed to be uniform or equal to zero. For the second item, the absorption factor has been taken as a constant. With these developments, the curl of the potential density becomes... 

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