The negative log-likelihood function
\begin{align} \text{min}_B -log|\Sigma^{-1}| + \text{tr}[(Y-XB)\Sigma^{-1}(Y-XB)] \end{align}
is a convex optimization with respect to $\Sigma^{-1}$. However, if I have a constraint:
\begin{equation} \Sigma = (J + BU')W(J + BU')' \end{equation}
is this still a convex optimization problem? Except for B, the rest of the quantities are known.