A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements
arXiv:1506.06081v3191 citations
Originality Incremental advance
AI Analysis
This provides a scalable solution for low-rank matrix recovery, which is incremental as it builds on existing nonconvex optimization methods.
The authors tackled the rank minimization problem and semidefinite programming by proposing a gradient descent algorithm that converges linearly to the global optimum with O(r^3 κ^2 n log n) random measurements.
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 $O(r^3 κ^2 n \log n)$ random measurements of a positive semidefinite $n \times n$ matrix of rank $r$ and condition number $κ$, our method is guaranteed to converge linearly to the global optimum.