Publication: A new framework for the computation of Hessians
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

A new framework for the computation of Hessians

- Article in a journal -
 

Author(s)
R. M. Gower , M. P. Mello

Published in
Optimization Methods and Software

Year
2012

Abstract
We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on Griewank and Walther's [Evaluating derivatives, in Principles and Techniques of Algorithmic Differentiation, 2nd ed., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008] state transformations synthesizes the calculation of the Hessian as a formula. These dual points of view, graphical and algebraic, lead to a new framework for Hessian computation. This is illustrated by developing edge_pushing, a new truly reverse Hessian computation algorithm that fully exploits the Hessian's symmetry. Computational experiments compare the performance of edge_pushing on 16 functions from the CUTE collection [I. Bongartz et al. Cute: constrained and unconstrained testing environment, ACM Trans. Math. Softw. 21(1) (1995), pp. 123–160] against two algorithms available as drivers of the software ADOL-C [A. Griewank et al. ADOL-C: A package for the automatic differentiation of algorithms written in C/C++, Technical report, Institute of Scientific Computing, Technical University Dresden, 1999. Updated version of the paper published in ACM Trans. Math. Softw. 22, 1996, pp. 131–167; A. Walther, Computing sparse Hessians with automatic differentiation, ACM Trans. Math. Softw. 34(1) (2008), pp. 1–15; A.H. Gebremedhin et al. Efficient computation of sparse Hessians using coloring and automatic differentiation, INFORMS J. Comput. 21(2) (2009), pp. 209–223], and the results are very promising.

AD Tools
ADOL-C

AD Theory and Techniques
Hessian

BibTeX
@ARTICLE{
         Gower2012Anf,
       author = "Gower, R. M. and Mello, M. P.",
       title = "A new framework for the computation of {H}essians",
       journal = "Optimization Methods and Software",
       volume = "27",
       number = "2",
       pages = "251--273",
       year = "2012",
       doi = "10.1080/10556788.2011.580098",
       url = "http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.580098",
       eprint = "http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.580098",
       abstract = "We investigate the computation of Hessian matrices via Automatic Differentiation,
         using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved
         in calculating the Hessian. The algebraic model, based on Griewank and Walther's [Evaluating
         derivatives, in Principles and Techniques of Algorithmic Differentiation, 2nd ed., Society for
         Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008] state transformations synthesizes
         the calculation of the Hessian as a formula. These dual points of view, graphical and algebraic,
         lead to a new framework for Hessian computation. This is illustrated by developing edge_pushing, a
         new truly reverse Hessian computation algorithm that fully exploits the Hessian's symmetry.
         Computational experiments compare the performance of edge_pushing on 16 functions from the CUTE
         collection [I. Bongartz et al. Cute: constrained and unconstrained testing environment, ACM Trans.
         Math. Softw. 21(1) (1995), pp. 123–160] against two algorithms available as drivers of the
         software ADOL-C [A. Griewank et al. ADOL-C: A package for the automatic differentiation of
         algorithms written in C/C++, Technical report, Institute of Scientific Computing, Technical
         University Dresden, 1999. Updated version of the paper published in ACM Trans. Math. Softw. 22,
         1996, pp. 131–167; A. Walther, Computing sparse Hessians with automatic differentiation,
         ACM Trans. Math. Softw. 34(1) (2008), pp. 1–15; A.H. Gebremedhin et al. Efficient
         computation of sparse Hessians using coloring and automatic differentiation, INFORMS J. Comput.
         21(2) (2009), pp. 209–223], and the results are very promising.",
       ad_tools = "ADOL-C",
       ad_theotech = "Hessian"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)