Is there a closed-form solution for this problem?
$$\begin{array}{ll} \text{minimize} & {\color{red}x}^{T}A^{T}A{\color{red}x} \\ \text{subject to} & \left\Vert {\color{red}x}\right\Vert_2^2 = 1\\ & 0_n \le A {\color{red}x}\le \delta 1_n\end{array}$$
where $\delta > 0$ is given, $A$ is full-rank $n \times n$ square matrix and $A^TA$ is positive definite.
Without the second constraint the solution would be the eigenvector associated with the smallest eigenvalue. But what happens when we have the second constraint? Is there a closed-form solution in terms of the eigenvectors?
Thanks!