We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With O(r 3 \kappa 2 n \log n) random measurements of a positive semidefinite n\times n matrix of rank r and condition number \kappa, our method is guaranteed to converge linearly to the global optimum.

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r 3 \kappa 2 n \log n)$ random measurements of a positive semidefinite $n\times n$ matrix of rank $r$ and condition number $\kappa$, our method is guaranteed to converge linearly to the global optimum. Papers published at the Neural Information Processing Systems Conference.