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arXiv · 1506.06081

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

Qinqing Zheng·John Lafferty
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Abstract

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.

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Qinqing Zheng, John Lafferty. 2015-06-19. A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements. https://arxiv.org/abs/1506.06081

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