Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version

@article{Zheng2022RiemannianOU,
  title={Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version},
  author={Shixin Zheng and Wen Huang and Bart Vandereycken and Xiangxiong Zhang},
  journal={ArXiv},
  year={2022},
  volume={abs/2204.07830}
}
We consider smooth optimization problems with a Hermitian positive semi-definite fixed-rank constraint, where a quotient geometry with three Riemannian metrics g i ( · , · ) ( i = 1 , 2 , 3) is used to represent this constraint. By taking the nonlinear conjugate gradient method (CG) as an example, we show that CG on the quotient geometry with metric g 1 is equivalent to CG on the factor-based optimization framework, which is often called the Burer–Monteiro approach. We also show that CG on the… 

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