I have the following quadratically-constrained linear program (QCLP)
$$ \begin{array}{ll} \underset {x} {\text{minimize}} & -c^T x \\ \text{subject to} & x^T Q x \leq a^2 \\ & x^T L x = 1 \end{array} $$
where $Q$ and $L$ are both symmetric positive definite matrices.
I know how to solve this problem when the 2nd constraint is absent but with the additional constraint I'm unable to get a closed form solution. Does such a solution exist? If not, are there any numerical algorithms which can exploit this problem structure?