Sorry to bother you again, hopefully someone will answer again...
I have some questions about optimisation problems, related to KT conditions (but maybe not only). My questions are rather theoretical, I believe, so no calculations.
Suppose I have to find, if existent, max and min of $f(x, y, z)$ subject to one or more constraints (let's say $g(x) \leq b$ and $h(x) = 0$ or $h(x) \leq c$), but subject also to the positivity of the variabiles: $x\geq 0, y \geq 0, z\geq 0$.
Here are the questions:
Supposedly, this resembles a KT problem. Is there some reason for which I cannot solve the problem as if I had only the constraint(s), ignoring hence $x, y, z \geq 0$, and only at the end check if they respect the conditions $x, y, z \geq 0$?
If non active constraints are "useless", why do I have to check them the same?
This for the moment. The most important question is the first one, because I tried to do that with some exercise, but I cannot conclude...