Approximating sparse Hessian matrices using large-scale linear least squares

Author:

Fowkes Jaroslav M.,Gould Nicholas I. M.,Scott Jennifer A.

Abstract

AbstractLarge-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.

Funder

Engineering and Physical Sciences Research Council

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics

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