I want to solve the following large scale convex problem:
$min\ \ ||A$u-b$||_2^{2}+ ||$U$_{(1)}||_*+||$U$_{(2)}||_*+||$U$_{(3)}||_*$
where U is a three order tensor, U$_{(i)}$ is a matrix whose column are the mode-$i$ fibers of U(i=1,2,3),u is vec(U).
The software 'cvx' can solve this problem, but it can not deal with the large scale problem, I read some papers but I can't implement them, is there any software to do this?