It is pretty well-known that the minimisation of the nuclear norm (sum of all singular values) is closely related to semidefinite programming.
However, I struggle to find a way to rewrite the problem "minimise $\|A\|_{\ast},$ the nuclear norm, subject to $A \in \mathcal A$" into the form "minimise $f(B)$ subject to $B \geq 0, g(B) \in \mathcal A$" where $f,g$ are linear.
Does anyone have a reference or know a brief answer?