Does it make sense to use the KKT conditions to transform an optimization problem with a large number of inequality constraints into an unconstrained optimization problem? I don't yet fully understand the KKT formulation, however I have seen a factor of $2^n$ mentioned. So before I spend more time investigating KKT, is it feasible to use for a system of say 50 inequality constraints?
To give more detail, I have $N+1$ constraints with the following form:
$C_1$: $\sum_{i=1}^N x_i \le Q$
$C_2...C_{N+1}$: $C_i \ge 0$; $i=1...N$
Does KKT infer I have to investigate $2^{N+1}$ possibilities?