I want to solve following optimization problem in $x \in \mathbb R^n$.

$$\begin{array}{ll} \text{maximize} & \displaystyle\sum_i(x M_i x^T)^2\\ \text{subject to} & \|x\|_2 = 1\end{array}$$

where matrices $M_i$ are **not** positive semidefinite.

Is it even convex problem and is there a solution in closed form?