I would like to rewrite this two-level program as a Non Linear Program using KKT conditions
$\min_{x \in X, \space y \in Y} \space f(x)$
$\text{s.t. } \space g(x, y) \leq 0$
$y \in \text{argmin}_{z \in Y} \space F(x,z)$
$\space \space \space \space \space \space \text{s.t.} \space Ax + Bz - b \leq 0$
Here $A$ and $B$ are matrices with dimension $m \times n_x$ and $m \times n_y$ respectively. The idea is to replace the $\text{argmin}$ constraint on the $y$ variables with KKT conditions for a point $(x,y)$.