Example of an optimum FJ point which is not a KT point The Kuhn-Tucker conditions talk about what locally optimum points in a non linear program satisfy WHEN the gradient of the active restrictions in said points are linearly independent.
However, this opens the possibility of an optimum showing up which is not a KT point, if in such a point the gradients are linearly dependent.
Such a point would necessarily have to be a Fritz John point, if I have understood correctly.
Can somebody give me such an example?

Consider the problem 
$$\min f(x)=x,\;s.t \; h_1(x)= x^2=0,\;h_2(x)=x^4=0.$$ The obvious minimum is $x=0.$ This point is not KT, however it is certainly FJ. 
