I am having trouble writing code for this problem. Suppose I wanted to solve the following optimization problem

\begin{align}

\min_Z ||Z||*{*}+||v^TZ||^2 \
\text{subject to } Z*{i,j}=A_{i,j} ~\forall{i,j\in\Omega}

\end{align}

Here vector v, and matrix A are fixed and provided as parameters.

How do I go about solving this. Perhaps it is pretty easy to do it using tfocs, but I am unable to do it. Any help, pointers will be deeply appreciated.