English

Comment on "First-order methods almost always avoid strict saddle points"

Optimization and Control 2022-04-04 v1

Abstract

The analysis on the global stability of Riemannian gradient descent method in manifold optimization (i.e., it avoids strict saddle points for almost all initializations) due to Lee et al. (Math. Program. 176:311-337) is corrected. Moreover, an explicit bound on the step-size is presented by the newly introduced retraction L-smooth property.

Keywords

Cite

@article{arxiv.2204.00521,
  title  = {Comment on "First-order methods almost always avoid strict saddle points"},
  author = {Jinyang Zheng and Yong Xia},
  journal= {arXiv preprint arXiv:2204.00521},
  year   = {2022}
}

Comments

7 pages

R2 v1 2026-06-24T10:34:51.748Z