A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements

摘要

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~3k~2n log n) random measurements of a positive semidefinite n×n matrix of rank r and condition number k, our method is guaranteed to converge linearly to the global optimum.