is there any way to solve the following problem with a quadratic objective and a second-order cone constraint in closed form?
$$\min_{x\in\mathbb{R}^d} (x-x_0)^TA(x-x_0) \\\text{subject to } \sqrt{x^T\Sigma x} + \mu^\top x\leq 0 $$
with $\Sigma$ and $A$ Positive Semi-Definite matrices and $x_0,\mu \in \mathbb{R}^d$.