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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A new framework for the computation of Hessians

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Author(s):
Gower, R. M. [1] ; Mello, M. P. [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Appl Math, Sao Paulo - Brazil
Total Affiliations: 1
Document type: Journal article
Source: OPTIMIZATION METHODS & SOFTWARE; v. 27, n. 2, SI, p. 251-273, 2012.
Web of Science Citations: 7
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. (AU)

FAPESP's process: 06/53768-0 - Computational methods of optimization
Grantee:José Mário Martinez Perez
Support type: Research Projects - Thematic Grants
FAPESP's process: 09/04785-7 - Automatic differentiation of Hessian matrices
Grantee:Robert Mansel Gower
Support type: Scholarships in Brazil - Master