@article{29c2c9aff8684a65927d3932ae533372,
title = "Nearly optimal bounds for the global geometric landscape of phase retrieval",
abstract = "The",
keywords = "geometric landscape, nonconvex optimization, phase retrieval",
author = "Cai, \{Jian Feng\} and Meng Huang and Dong Li and Yang Wang",
note = "Publisher Copyright: {\textcopyright} ,j=1,...,m . A natural least squares formulation can be used to solve this problem efficiently even with random initialization, despite its non-convexity of the loss function. One way to explain this surprising phenomenon is the benign geometric landscape: (1) all local minimizers are global; and (2) the objective function has a negative curvature around each saddle point and local maximizer. In this paper, we show that m=O(nlogn) Gaussian random measurements are sufficient to guarantee the loss function of a commonly used estimator has such benign geometric landscape with high probability. This is a step toward answering the open problem given by Sun et al (2018 Found. Comput. Math. 18 1131-98), in which the authors suggest that O(nlogn) or even O(n) is enough to guarantee the favorable geometric property.",
year = "2023",
month = jul,
doi = "10.1088/1361-6420/acdab7",
language = "英语",
volume = "39",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "Institute of Physics",
number = "7",
}