Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918362803601408 |
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| author | Daas, Hussam Al Gould, Nicholas I. M. |
| author_facet | Daas, Hussam Al Gould, Nicholas I. M. |
| contents | We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a very-low-dimensional subspace as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a basis spanning these solutions using an efficient extended-Krylov-subspace iteration that involves a single matrix factorization. The problems within the subspace using such a basis may be solved at very low cost using effective high-order root-finding methods. This then provides an alternative to common methods using multiple factorizations or standard Krylov subspaces. We provide numerical results to illustrate the effectiveness of our TREK/NREK approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems Daas, Hussam Al Gould, Nicholas I. M. Numerical Analysis Optimization and Control We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a very-low-dimensional subspace as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a basis spanning these solutions using an efficient extended-Krylov-subspace iteration that involves a single matrix factorization. The problems within the subspace using such a basis may be solved at very low cost using effective high-order root-finding methods. This then provides an alternative to common methods using multiple factorizations or standard Krylov subspaces. We provide numerical results to illustrate the effectiveness of our TREK/NREK approach. |
| title | Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2511.11135 |