I am facing the following optimization problem: $$ \max \|R^T A R\|_F \\ s.t. R^T R = I $$ That is, maximize the frobenius norm of the qudaratic form $R^T A R$ where $R$ is a orthonormal matrix.
$A \in \mathbb{R}^{n\times n}$ is a real symmetric matrix. $R\in \mathbb{R}^{n\times m}$ where $m < n$.
- The objective can be transformed to $tr(R^T A R R^T A R)$.
- If the frobenius norm is replaced by the trace operator ($\max tr(R^T A R)$), then the problem can be solved with eigen-decomposition. But I don't know how to solve the frobenius norm case.
Any ideas or comments will be appreciated. Thanks!