min $2x_1^2+2x_2^2+4x$
s.t g-$x_1^2+x_2^2-4\leq0$
h-$x_1^2+x_2^2-4x_1+3\leq0$
solve with KKT
I've found that the KKT point are (1,0),(2,0) and I wanted to find the non-regular point where the gradients of $h,g$ are linearly dependent but I get the following :
$$a\nabla g+b\nabla h=a2x_1+b2x_1-4b=0,ax_2+bx_2=0$$
And if $a\neq-b$ $x_1=\frac{2b}{a+b},x_2=0$ can cause the gradients to be always 0 so I have infinite solutions. where am I wrong here?