Suppose $A \in R^{n \times n}$ and that $A$ is invertible, derive the directions generated by the Newton Method for the following problem
$\min_{y \in R^n} f(Ay)$
I know what it means now but am stuck. I think I have found the gradient but am stuck with the Hessian. Gradient should be $\nabla f(Ay)^T A$ but what about the Hessian?
Let $g(y) = f(Ay)$. The Newton direction is $\Delta x = -H_g(y)^{-1} D_g(y)$. By application of the chain rule, $D_g(y) = A^TD_f(Ay)$ and $H_g(y) = A^TH_f(Ay)A$, so
$$\Delta x = -(A^TH_f(Ay)A)^{-1} (A^TD_f(Ay))=-A^{-1}H_f(Ay)^{-1}D_f(Ay).$$