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math.OC2021★ 1 cited
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical poi…
math.OC2019★ 3 cited
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
In this paper, we provide some analysis on the asymptotic escape of strict saddles in manifold optimization using the projected gradient descent (PGD) algorithm. One of our main co…