SOLVING SYSTEMS OF PHASELESS EQUATIONS VIA RIEMANNIAN OPTIMIZATION WITH OPTIMAL SAMPLING COMPLEXITY

作     者：Jianfeng Cai Ke Wei Jianfeng Cai;Ke Wei

作者机构：Department of MathematicsHong Kong University of Science and TechnologyClear Water BayKowloonHong Kong SARChina School of Data ScienceFudan UniversityShanghaiChina 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2024年第42卷第3期

页      面：755-783页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Phaseless equations Riemannian gradient descent Manifold of rank-1 and positive semidefinite matrices Optimal sampling complexity 

摘      要：A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=*** algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite *** recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of *** key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear *** evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.