Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

Harry Oviedo ()
Additional contact information
Harry Oviedo: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diag. Las Torres 2640, Santiago de Chile 7941169, Chile

Mathematics, 2023, vol. 11, issue 11, 1-17

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.

Keywords: proximal point method; Stiefel manifold; orthogonality constraint; Riemannian optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/11/2414/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/11/2414/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:11:p:2414-:d:1153538

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().