Solving Joint Diagonalization Problems via a Riemannian Conjugate Gradient Method in Stiefel Manifold

Urdaneta, Hugo Lara; Oviedo, Harry

doi:10.5540/03.2018.006.02.0327

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Cited by 3 publications

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“…It can be easily shown that the operator (6) effectively projects matrices from R n×p to the tangent space T X St(n, p). This projection operator was also considered in [27].…”

Section: Preliminariesmentioning

confidence: 99%

Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

Oviedo

2023

Mathematics

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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.

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“…It can be easily shown that the operator (6) effectively projects matrices from R n×p to the tangent space T X St(n, p). This projection operator was also considered in [27].…”

Section: Preliminariesmentioning

confidence: 99%