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A sparse quasi-Newton update derived variationally with a nondiagonally weighted Frobenius norm


Author: Ph. L. Toint
Journal: Math. Comp. 37 (1981), 425-433
MSC: Primary 65F30; Secondary 15A24, 65K10
DOI: https://doi.org/10.1090/S0025-5718-1981-0628706-6
MathSciNet review: 628706
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Abstract: The problem of symmetric sparse updating is considered from a variational point of view and a new class of sparse symmetric quasi-Newton updating formulae is derived. This class results from the use of a nondiagonally weighted Frobenius norm. The computation of the update involves only one positive definite and symmetric linear system that has the same sparsity pattern as the problem itself.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0628706-6
Keywords: Nonlinear optimization, sparsity, matrix updating
Article copyright: © Copyright 1981 American Mathematical Society