can someone point me to the direction how to calculate the derivatives of a sum of singular values of a matrix?
I am trying to minimize
$$\min_A \parallel A \parallel_*+ \cdots $$ where $\parallel A \parallel_*=\sum_i \sigma_i$ is the sum of the singular values of $A$.

This is motivated by this [paper][1].

Thank you very much!


  [1]: https://papers.nips.cc/paper/3704-robust-principal-component-analysis-exact-recovery-of-corrupted-low-rank-matrices-via-convex-optimization.pdf