Reviews: The non-convex Burer-Monteiro approach works on smooth semidefinite programs

This paper considers a specific class of semi-definite programs (minimize linear objective subject to linear equally and positive semi-definiteness constraints). This convex optimization problem is replaced by a non convex one where the optimization variable is replaced by the outer product of a matrix and its transpose. The paper shows that under certain conditions (size of the factorization large enough. More specifically, the paper is very closely related to prior work by Burer and Monteiro. I think [1] proposed the change of variables X YY T, proposed also an BFGS augmented Lagrangian algorithm for solving the nonconvex problem, and showed experimentally that it reliably gives a global minimum if number of columns of Y is large enough.