So I have this exercise I found in old exams.
Using KKT conditions solve the optimization problem ($, P, min) where
f(x,y) = x^2 + (y-4)^2, and
$ = {(x,y) from R^2; x + 3y <= 10 and x -2y <= 1 and x^2-4x+y <= 0}
I used 3 KKT conditions and got this equations:
Lx = 2x + &1 + &2 + 2&3 * x -4&3 = 0;
Ly = 2y - 8 + 3&1 + 2&2 + &3 = 0;
&1(x+3y-10) = 0;
&2(x-2y-1) = 0;
&3(x^2-4x+y) = 0;
where &i is lambda with index i;
So now what? Do I have to check for every constraint whether it is active or not? But that is 8 options... is there another way?