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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On variable-metric methods for sparse Hessians

Author: D. F. Shanno
Journal: Math. Comp. 34 (1980), 499-514
MSC: Primary 65K10; Secondary 15A57, 90C30
MathSciNet review: 559198
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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.

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Article copyright: © Copyright 1980 American Mathematical Society