I am solving this optimization problem: \begin{equation} \min (x-4)^2+y^2 \end{equation} subject to
\begin{cases} x^2+y^2-9\le0 \\ -x-3\le0\\ x-3\le0\\ -y-2\le0 \end{cases} In the point (0,3) the first and the third constraints are active. However, their gradients are: $\nabla g_1=(6,0)$ and $\nabla g_2=(1,0)$ so they are not linearly independent hence KKT theorem cannot be applied. What should I do to qualify the point (3,0) has a minimum or a maximum?