For a problem I am working on I need to minimimize

$\displaystyle \sum_t || x^TA_tx - b_t||^2_2$,

with respect to $\displaystyle x \in R^n$. The matrix $\displaystyle A_t \in R^{n \times n}$ is not positive definite, $\displaystyle b_t \in R$.

Is there a closed form solution for this?

The norm can also be the L1 norm and does not need to be squared, if this simplifies the problem.

I would be very thankful if somebody could help!