Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

Autor:	Harry Oviedo
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	proximal point method Stiefel manifold orthogonality constraint Riemannian optimization Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 11, p 2414 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11112414
Popis:	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.
Databáze:	Directory of Open Access Journals
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