Approximating large-scale Hessian matrices using secant equations

Fowkes, J. M., Gould, N. I. M. and Scott, J. A. ORCID: https://orcid.org/0000-0003-2130-1091 (2025) Approximating large-scale Hessian matrices using secant equations. ACM Transactions on Mathematical Software (TOMS), 51 (2). 9. ISSN 1557-7295 doi: 10.1145/3728460

Abstract/Summary

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 too expensive for 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 collection for optimization illustrate the effectiveness and robustness of our proposed method.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/122164
Identification Number/DOI	10.1145/3728460
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Association for Computing Machinery (ACM)
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