Publication: On the Impact of Automatic Differentiation on the Relative Performance of Parallel Truncated Newton and Variable Metric Algorithms
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On the Impact of Automatic Differentiation on the Relative Performance of Parallel Truncated Newton and Variable Metric Algorithms

- Article in a journal -
 

Area
Optimization

Author(s)
Laurence C. W. Dixon

Published in
SIAM J. Optim.

Year
1991

Abstract
The sparse doublet method for obtaining the gradient of a function or the Jacobian of a vector will be described and contrasted with reverse automatic differentiation. Its extension, the sparse triplet method for finding the Hessian of a function, will also be described and the effect of using these within classic optimisation algorithms discussed. Results obtained using a parallel implementation of sparse triplet automatic differentiation of a partially separable function on the Sequent Balance will be presented. In this paper it is shown that: (bullet) automatic differentiation can no longer be neglected as a method for calculating derivatives; (bullet) sparse triplets provide an effective method that can be implemented in parallel for calculating the Hessian matrix; (bullet) this approach can be combined effectively with the truncated Newton method when solving large unconstrained optimisation problems on parallel processors.

AD Theory and Techniques
Hessian, Parallelism

BibTeX
@ARTICLE{
         Dixon1991OtI,
       author = "Laurence C. W. Dixon",
       title = "On the Impact of Automatic Differentiation on the Relative Performance of Parallel
         Truncated {N}ewton and Variable Metric Algorithms",
       journal = "SIAM J. Optim.",
       pages = "475--486",
       key = "Dixon1991OtI",
       referred = "[More2001ADT].",
       year = "1991",
       volume = "1",
       abstract = "The sparse doublet method for obtaining the gradient of a function or the Jacobian
         of a vector will be described and contrasted with reverse automatic differentiation. Its extension,
         the sparse triplet method for finding the Hessian of a function, will also be described and the
         effect of using these within classic optimisation algorithms discussed. Results obtained using a
         parallel implementation of sparse triplet automatic differentiation of a partially separable
         function on the Sequent Balance will be presented. In this paper it is shown that: (bullet)
         automatic differentiation can no longer be neglected as a method for calculating derivatives;
         (bullet) sparse triplets provide an effective method that can be implemented in parallel for
         calculating the Hessian matrix; (bullet) this approach can be combined effectively with the
         truncated Newton method when solving large unconstrained optimisation problems on parallel
         processors.",
       keywords = "automatic differentiation; parallel computation; optimisation",
       url = "http://link.aip.org/link/?SJE/1/475/1",
       doi = "10.1137/0801028",
       ad_area = "Optimization",
       ad_theotech = "Hessian, Parallelism"
}


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