Article Outline
Keywords
The Forward Mode
Illustrative Example 1: Forward Mode
The Mixed Method
Illustrative Example 2: Reverse Differentiation
Reverse Method
Illustrative Example 3: Reverse Gradient, Forward Hessian
See also
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bartholomew-Biggs MC Optima library. Numerical Optim. Centre Univ. Hertfordshire, England
Berz M, Bischof Ch, Corliss G, Griewank A (eds) (1996) Computational differentiation: techniques, applications, and tools. SIAM, Philadelphia
Bischof Ch, Carle A (1996) Users' experience with ADIFOR 2.0. In: Berz M, Bischof Ch, Corliss G, Griewank A (eds) Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia, pp 385–392
Christianson DB (1992) Automatic Hessians by reverse accumulation. IMA J Numer Anal 12:135–150
Christianson DB, Davies AJ, Dixon LCW, Zee P Van der, (1997) Giving reverse differentiation a helping hand. Optim Methods Softw 8:53–67
Christianson DB, Dixon LCW, Brown S (1996) Sharing storage using dirty vectors. In: Berz M, Bischof Ch, Corliss G, Griewank A (eds) Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia, pp 107–115
Dixon LCW (1993) On automatic differentiation and continuous optimization. In: Spedicato E (ed) Algorithms for continuous optimization: the state of the art. NATO ASI series. Kluwer, Dordrecht, pp 501–512
Dixon LCW, Maany Z, Mohsenina M (1989) Experience using truncated Newton for large scale optimization. In: Bromley K (ed) High Speed Computing, vol 1058. SPIE–The Internat. Soc. for Optical Engineering, Bellingham, WA, pp 94–104
Dixon LCW, Maany Z, Mohseninia M (1990) Automatic differentiation of large sparse systems. J Econom Dynam Control 14(2)
Griewank A (1989) On automatic differentiation. In: Iri M, Tanabe K (eds) Mathematical programming: recent developments and applications. Kluwer, Dordrecht, pp 83–108
Griewank A (1992) Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim Methods Softw 1:35–54
Kubota K (1991) PADRE2, A FORTRAN precompiler yielding error estimates and second derivatives. In: Griewank A and Corliss GF (eds) Automatic differentiation of algorithms: theory, implementation, and application. SIAM, Philadelphia, pp 251–262
Maany ZA (1989) Ada automatic differentiation packages. Techn Report Hatfield Polytechnic NOC TR224
Rall LB (1981) Automatic differentiation: techniques and applications. Lecture Notes Computer Sci, vol 120. Springer, Berlin
Shiriaev D (1993) Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment. PhD Thesis Inst Angew Math Univ Karlsruhe
Shiriaev D, Griewank A (1996) ADOL–F Automatic differentiation of Fortran codes. In: Berz M, Bischof Ch, Corliss G, Griewank A (eds) Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia, pp 375–384
Wengert RE (1964) A simple automatic derivative evaluation program. Comm ACM 7(8):463–464
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Dixon, L. (2008). Automatic Differentiation: Calculation of the Hessian . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_23
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering