Let $u \in \mathcal{R}^n$ be a vector of decision variables. Let $C(u)$ be a function $\mathcal{R}^n \to \mathcal{R}$ that is a measure of performance of the variables. Further, it is required that the final distribution of $u$ be normal , $u \sim \mathcal{N}(\mu,\sigma)$, for given values of $\mu$ and $\sigma$. How does one impose such a constraint on the final shape/ distribution of the design variables ?
$\underset{u}{min} \quad C(u) $
$ \text{S.T.} \quad u \sim \mathcal{N}(\mu,\sigma)$