Singular Values & the SVD · Superchallenge problem

Let $A = \begin{pmatrix}2 & 1 & 0\\1 & 2 & 0\\0 & 0 & -5\end{pmatrix}$. Find the minimum over all real $3\times 3$ matrices $B$ of $\dfrac12\|A - B\|_F^2 + 2\|B\|_*$, where $\|B\|_*$ is the nuclear norm (sum of singular values).