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math.OC2019★ 4 cited
First-order methods almost always avoid saddle points: the case of vanishing step-sizes
Ioannis Panageas, Georgios Piliouras, Xiao Wang
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some of the most commonly used first order methods almost surely (under random initializations) and with ste…
math.OC2015★ 137 cited
Low-rank Solutions of Linear Matrix Equations via Procrustes Flow
Stephen Tu, Ross Boczar, Max Simchowitz +2
In this paper we study the problem of recovering a low-rank matrix from linear measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate obtained…