I would like to characterize the distribution of the solutions of a convex quadratic program as the coefficient of the linear term and the rhs of the constraints vary.
I.e., if \begin{eqnarray} x &=& \arg \min_x \frac{1}{2} x' Q x + d' x \\ && s.t. \;\; A x \leq b \end{eqnarray}
when the problem is feasible.
And if $d$ and $b$ are independently distributed according to $d \sim \mathcal{N}(\mu_d, \Sigma_d)$ and $b \sim \mathcal{N}(\mu_b, \Sigma_b)$, can I say something about the distribution of $x$?
I can make progress on my problem if I can at least say something about the mean of $x$. Being able to characterize its covariance or higher moments would be even better.
I would appreciate it if someone can point me to a solution, or any relevant literature that suggests a plan of attack on this problem.