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

作　　者：Jianfeng Cai Ke Wei 

机构地区：[1]Department of Mathematics,Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong SAR,China [2]School of Data Science,Fudan University,Shanghai,China

出　　处：《Journal of Computational Mathematics》2024年第3期755-783,共29页计算数学（英文）

摘　　要：A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite matrices.Theoretical 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 unknowns.Two key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear operator.Empirical evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.

关 键 词：Phaseless equations Riemannian gradient descent Manifold of rank-1 and positive semidefinite matrices Optimal sampling complexity 

分 类 号：O18[理学—数学]