Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, we consider the problem of minimizing a continuously differentiable function on the Stiefel manifold. To solve this problem, we develop a geodesic-free proximal point algorithm equipped with Euclidean distance that does not require use of the Riemannian metric. The proposed method can be regarded as an iterative fixed-point method that repeatedly applies a proximal operator to an initial point. In addition, we establish the global convergence of the new approach without any restrictive assumption. Numerical experiments on linear eigenvalue problems and the minimization of sums of heterogeneous quadratic functions show that the developed algorithm is competitive with some procedures existing in the literature.

Original languageEnglish
Article number2414
Issue number11
StatePublished - Jun 2023
Externally publishedYes


  • Riemannian optimization
  • Stiefel manifold
  • orthogonality constraint
  • proximal point method


Dive into the research topics of 'Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold'. Together they form a unique fingerprint.

Cite this