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- Title
Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold.
- Authors
Oviedo, Harry
- Abstract
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.
- Subjects
EUCLIDEAN algorithm; RIEMANNIAN metric; DIFFERENTIABLE functions; EUCLIDEAN distance; PROBLEM solving; EIGENVALUES
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 11, p2414
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11112414