On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems.

摘要: The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, for general nonlinear measurements, novel named bound difference (BDP) introduced. Using RIP and BDP jointly, we propose new criterion to certify nonexistence rank-1 case, prove it leads much stronger theoretical guarantee than existing bounds on RIP.