# minimize frobenius norm subject to rank condition

I'm trying to solve the following problem: Let A be (a, b) matrix. Given l < min ( a, b) , solve:

\begin{align} \min_{rank(X)= l} || A - X ||_{Fro}^2 \end{align} I'm novice in optimization and don't know how to take the rank constraint into account. Thanks!

As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.

However, this particular problem has an analytic solution in terms of the SVD https://en.wikipedia.org/wiki/Low-rank_approximation