## On variable-metric methods for sparse Hessians

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- by D. F. Shanno PDF
- Math. Comp.
**34**(1980), 499-514 Request permission

## Abstract:

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis’s nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method is tested against the sparse PSB and variable-memory conjugate gradient methods, with computational experience uniformly favoring the sparse BFGS.## References

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## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp.
**34**(1980), 499-514 - MSC: Primary 65K10; Secondary 15A57, 90C30
- DOI: https://doi.org/10.1090/S0025-5718-1980-0559198-2
- MathSciNet review: 559198