Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems

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Persistent URL	http://purl.org/net/epubs/work/63577109
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Record Id	63577109
Title	Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems
Contributors	H Al Daas (STFC Rutherford Appleton Lab.), NIM Gould (STFC Rutherford Appleton Lab.)
Abstract	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 lie on a manifold of approximately very low rank as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a basis for this manifold 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.
Organisation	STFC , SCI-COMP
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	STFC Preprints STFC-P-2025-002, SIAM J Optimiz STFC, 2025.		STFC-P-2025-002.pdf	2025