Approximating sparse Hessian matrices using large-scale linear least squares

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Persistent URL	http://purl.org/net/epubs/work/54271845
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Record Id	54271845
Title	Approximating sparse Hessian matrices using large-scale linear least squares
Contributors	JM Fowkes (STFC Rutherford Appleton Lab.), NIM Gould (STFC Rutherford Appleton Lab.), J Scott (STFC Rutherford Appleton Lab.)
Abstract	Large-scale optimization algorithms frequently require sparse Hessian matrices that are not readily available. Existing methods for approximating large sparse Hessian matrices have limitations. To try and overcome these, we propose a novel approach that reformulates the problem as the solution of a large linear least squares problem. The least squares problem is sparse but can include a number of rows that contain significantly more entries than other rows and are regarded as dense. We exploit recent work on solving such problems using either the normal equations or an augmented system to derive a robust approach for computing approximate sparse Hessian matrices. Example sparse Hessians from the CUTEst test problem collection for optimization illustrate the effectiveness and robustness of the new method.
Organisation	STFC , SCI-COMP
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	STFC Preprints STFC-P-2023-003, Numer Algorithms STFC, 2023.		STFC-P-2023-003.pdf	2023