Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

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...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Mathematics (Basel) Ročník 11; číslo 11; s. 2414
Hlavný autor: Oviedo, Harry
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 23.05.2023
Predmet:
Algorithms
Eigenvalues
Euclidean geometry
Euclidean space
Fixed points (mathematics)
Iterative methods
Linear algebra
Manifolds (mathematics)
Mathematical analysis
Mathematics
Methods
Operators (mathematics)
Optimization
orthogonality constraint
proximal point method
Quadratic equations
Riemannian optimization
Stiefel manifold
ISSN:2227-7390, 2227-7390
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math11112414