Let $A \in \mathbb{R}^{m \times m}$ be an arbitrary matrix, and let $D \in \mathbb{R}^{m \times m}$ be a diagonal matrix. Is there a known way to solve problems of the form,?
$\min_{x,y \in \mathbb{R}^{m}} x^{\top}Ay \text{ s.t. } \lVert x \rVert = \lVert y \rVert = 1$ and $x^{\top}Dy = c$, for some constant $c \in \mathbb{R}$.
Thanks in advance.