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A Riemannian subspace BFGS trust region method

A Riemannian subspace BFGS trust region method Motivated by the subspace techniques in the Euclidean space, this paper presents a subspace BFGS trust region (RTR-SBFGS) algorithm to the problem of minimizing a smooth function defined on Riemannian manifolds. In each iteration of the RTR-SBFGS algorithm, a low-dimensional trust region subproblem is solved, which reduces the amount of computation significantly for large scale problems. A limited-memory variant of RTR-SBFGS, named LRTR-SBFGS, is introduced also. Both RTR-SBFGS and LRTR-SBFGS are proved to converge globally. Under some mild conditions, we establish the local linear convergence of these two methods. Numerical results demonstrate that, compared to the state-of-the-art algorithms, RTR-SBFGS and LRTR-SBFGS are effective methods and subspace techniques are suitable for Riemannian optimization problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

A Riemannian subspace BFGS trust region method

Wei, Hejie; Yang, Wei Hong; Chai, Yinsheng
Optimization Letters , Volume 17 (8) – Nov 1, 2023
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References (22)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
1862-4472
eISSN
1862-4480
DOI
10.1007/s11590-022-01964-9
Publisher site
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Abstract

Motivated by the subspace techniques in the Euclidean space, this paper presents a subspace BFGS trust region (RTR-SBFGS) algorithm to the problem of minimizing a smooth function defined on Riemannian manifolds. In each iteration of the RTR-SBFGS algorithm, a low-dimensional trust region subproblem is solved, which reduces the amount of computation significantly for large scale problems. A limited-memory variant of RTR-SBFGS, named LRTR-SBFGS, is introduced also. Both RTR-SBFGS and LRTR-SBFGS are proved to converge globally. Under some mild conditions, we establish the local linear convergence of these two methods. Numerical results demonstrate that, compared to the state-of-the-art algorithms, RTR-SBFGS and LRTR-SBFGS are effective methods and subspace techniques are suitable for Riemannian optimization problems.

Journal

Optimization Letters – Springer Journals

Published: Nov 1, 2023

Keywords: Subspace method; Riemannian optimization; RTR-SBFGS method; Vector transport

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