Some Numerical Result Using a Sparse Matrix Updating Formula in Unconstrained Optimization

Research output: Contribution to journalArticle

Abstract

This paper presents a numerical comparison between algorithms for unconstrained optimization that take account of sparsity in the second derivative matrix of the objective function. Some of the methods included in the comparison use difference approximation schemes to evaluate the second derivative matrix and other use an approximation to it which is updated regularly using the changes in the gradient. These results show what method to use in what circumstances and also suggest interesting future developments.
Original languageEnglish
Pages (from-to)839-851
Number of pages13
JournalMathematics Of Computation
Volume32
Issue number143
Publication statusPublished - 1978

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Unconstrained Optimization
Sparse matrix
Second derivative
Updating
Derivatives
Difference Approximation
Numerical Results
Numerical Comparisons
Approximation Scheme
Difference Scheme
Sparsity
Gradient
Evaluate
Approximation

Cite this

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title = "Some Numerical Result Using a Sparse Matrix Updating Formula in Unconstrained Optimization",
abstract = "This paper presents a numerical comparison between algorithms for unconstrained optimization that take account of sparsity in the second derivative matrix of the objective function. Some of the methods included in the comparison use difference approximation schemes to evaluate the second derivative matrix and other use an approximation to it which is updated regularly using the changes in the gradient. These results show what method to use in what circumstances and also suggest interesting future developments.",
author = "Philippe Toint",
year = "1978",
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Some Numerical Result Using a Sparse Matrix Updating Formula in Unconstrained Optimization. / Toint, Philippe.

In: Mathematics Of Computation, Vol. 32, No. 143, 1978, p. 839-851.

Research output: Contribution to journalArticle

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