How to solve the problem using CVX.
We have a few observations of a matrix. Lets denote it by “D”. Since the observations are not accurate and some measurement error is involved, I want to solve this optimization problem: -
min_Z ||Z||_N such that ||E.*Z-D||_F<= epsilon.
Here Z is a matrix variable of dimension same as D.
E.*Z is the hadamard product of Z with E. And E represents the measurement matrix.
|| ||_N represents nuclear norm.
|| ||_F represents frobenious norm.
Now I typed something like this in my matlab code: -
cvx_begin sdp variable Z(m,n) semidefinite; norm(G.*Z(m,n)-D,'fro') <= epsilon ; minimize(norm_nuc(Z(m,n))) cvx_end
Its not working. I think I made some mistake. I will be really grateful if someone show me the right way to implement the optimization using CVX.