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Approximating sparse Hessian matrices using large-scale linear least squares.

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Title: Approximating sparse Hessian matrices using large-scale linear least squares.
Authors: Fowkes, Jaroslav M., Gould, Nicholas I. M., Scott, Jennifer A.
Source: Numerical Algorithms; Aug2024, Vol. 96 Issue 4, p1675-1698, 24p
Subject Terms: HESSIAN matrices, SPARSE matrices, OPTIMIZATION algorithms, LEAST squares, PROBLEM solving
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. [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
Description
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. [ABSTRACT FROM AUTHOR]
ISSN:10171398
DOI:10.1007/s11075-023-01681-z