# Sum of nuclear norms

Hi All,

How do I implement the sum of nuclear norms of a 3-D matrix in cvx?

Let X be a 3D matrix. I need to minimize the sum of the nuclear norm of each of the 2D matrix of X. i.e., minimize \sum (||X(:,:,i)||_{nuc})? where i is the index running through the number of 2D matrices

CVX throws an error when I tried implemented this: sum(nuc_norm(X(:,:,i)))

norm_nuc doesn’t have a vectorized analtog to norms . But you could use a brute force approach in which norm_nuc(X(:,:,i)) is evaluated inside a for loop indexed by i. If someone knows a nicer way to accomplish this, please post it.

Thank you