$\mu_E$ is a $4 \times 1$ vector composed of known constants, and $\mu$ is a vector of the same dimension but with unknown variables. Let us say $\mu = (x_1, x_2, x_3, x_4)^T$.
What is the meaning of the following notation in optimization?
minimize $|\mu_E - \mu|_2 $ subject to some constraints.
If you're wondering about the $| x |_2$-part, it is the usual ($l^2$-)norm of vectors. In general one writes $$|x|_p=\Big(\sum_{i=1}^n x_i^p \Big)^{1/p}$$ where $x$ is a vector in $\mathbb{R}^n$ and $x_i$ are its coordinates.