I've been struggling with this optimization problem using Matlab, I would really appreciate it if you could tell me how to solve it with Matlab, or at least which optimization method can solve it.
\begin{equation} \displaystyle \min_{A} ||(\hat{A}-A)\odot M||\substack F\\s.t. rank(A)=6 \end{equation}
M is a matrix of ones and zeros, the multiplication is pointwise. So I need to find the closest matrix A to A_hat in Frobenius norm which have effect only where the elements of M are ones, and with the constraint that rank(A) = 6