Solving Weighted Orthogonal Procrustes Problems via a Projected Gradient Method
This paper proposes a family of line--search methods to deal with weighted orthogonal procrustes problems. In particular, the proposed family uses a search direction based on a convex combination between the Euclidean gradient and the Riemannian gradient of the cost function. The non--monotone line-...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2024-11-01
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| Series: | Trends in Computational and Applied Mathematics |
| Subjects: | |
| Online Access: | https://tema.sbmac.org.br/tema/article/view/1786 |
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| Summary: | This paper proposes a family of line--search methods to deal with weighted orthogonal procrustes problems. In particular, the proposed family uses a search direction based on a
convex combination between the Euclidean gradient and the Riemannian gradient of the cost function. The non--monotone line--search of Zhang and Hager, and an adaptive
Barzilai--Borwein step--size are the chosen tools, in order to speed up the convergence of the
new family of methods. One of the extremes of that convex combination is reduced to well--known spectral projected gradient method, while the another one can be interpreted as
a Riemannian steepest descent method. To preserve feasibility of all the iterates, we use a
projection operator based on the singular value decomposition, which can be computed
efficiently via the spectral decomposition of an appropriate matrix. In addition, we prove that
the entire uncountable collection of search directions satisfies a descent condition.
Some numerical experiments are provided in order to demonstrate the effectiveness of the new approach. |
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| ISSN: | 2676-0029 |