Approximating large-scale Hessian matrices using secant equations

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Persistent URL	http://purl.org/net/epubs/work/58264684
Record Status	Checked
Record Id	58264684
Title	Approximating large-scale Hessian matrices using secant equations
Contributors	JM Fowkes (STFC Rutherford Appleton Lab.), NIM Gould (STFC Rutherford Appleton Lab.), JA 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 either do not impose sparsity or are computationally prohibitive. To try and overcome these limitations, we propose a novel approach that seeks to satisfy as many componentwise secant equations as necessary to define each row of the Hessian matrix. A naive application of this approach is prohibitively expensive on Hessian matrices that have some relatively dense rows but by carefully taking into account the symmetry and connectivity of the Hessian matrix we are able devise an approximation algorithm that is fast and efficient with scope for parallelism. Example sparse Hessian matrices from the CUTEst test problem collection for optimization illustrate the effectiveness and robustness of our proposed 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-2024-001, ACM Trans Math Software STFC, 2024.		STFC-P-2024-001.pdf	2024