For $X = (x_1^T,\ldots,x_N^T)^T \in \mathbb{R}^{Nm \times 1}$, where $x_i \in \mathbb{R}^{m \times 1}$ for $i \in \{1,\ldots,N\}$, $A \in \mathbb{R}^{r \times Nm}$, and $r \geq Nm$, I want to obtain a closed form solution of 

$$\max_{X \in \mathbb{R}^{Nm}}\{\|AX\|: \|x_i\|^2=1\}$$

where $\|\cdot\|$ denotes the Euclidean norm. I know how to find a closed form solution of

$$\max_{X \in \mathbb{R}^{Nm}}\{\|AX\|: \|X\|^2=1\}$$ 

that is, when $\|X\|^2=1$. However, I do not see how to solve it when we have $\|x_i\|^2=1$.