I have to minimize $f(x)=x^4-24x^2$ starting on the point $x\_o=1$. The method converge to $x=0$, but i know that the solution is $x=+-2\sqrt{3}$. The hessian and the derivate of the function are $C\_2$-smooth. $H[f(x)]^{-1}=\frac{1}{12x^2-48}$.


The method that i am using is: $x\_{k+1} = x\_k - H[f(x\_k)]^{-1}\*\nabla f(x\_k)$.



Newton's minimizing method converge to local maximum
Newton's is not really a "minimizing method". If you're using Newton's method to find a root of $f'$, the root you find might be a local minimum, local maximum or neither. To remove the root $x=0$ from consideration, you might try finding a root of $f'(x)/x$ instead.


