Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certification

Gavin Zhang, Salar Fattahi, Richard Y. Zhang

We consider using gradient descent to minimize the nonconvex function $f(X)=\ddot{I}•(X{X}^T)$ over an $n\times r$ factor matrix $X$, in which $\ddot{I}•$ is an underlying smooth convex cost fun…