Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval

Yuxin Chen Yuejie Chi Jianqing Fan Cong Ma

Optimization and Control mathscidoc:1912.43334

arXiv preprint arXiv:1803.07726
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest \mathbf {x}^{atural}\in\mathbb {R}^{n} from \mathbf {x}^{atural}\in\mathbb {R}^{n} quadratic equations/samples \mathbf {x}^{atural}\in\mathbb {R}^{n} , \mathbf {x}^{atural}\in\mathbb {R}^{n} . This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning.
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@inproceedings{yuxingradient,
  title={Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval},
  author={Yuxin Chen, Yuejie Chi, Jianqing Fan, and Cong Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113755869479894},
  booktitle={arXiv preprint arXiv:1803.07726},
}
Yuxin Chen, Yuejie Chi, Jianqing Fan, and Cong Ma. Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval. In arXiv preprint arXiv:1803.07726. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113755869479894.
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