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 Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 11, Pages 1923–1949 (Mi zvmmf376)

Fast automatic differentiation as applied to the computation of second derivatives of composite functions

E. S. Zasukhina

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: A technique for deriving formulas for the second derivatives of a composite function with constrained variables is proposed. The original system of constraint equations is associated with a linear system of equations, whose solution is used to determine the Hessian of the function. The resulting formulas are applied to discrete problems obtained by approximating optimal control problems with the use of Runge–Kutta methods of various orders. For a particular optimal control problem, the numerical results obtained by the gradient method and Newton's method with the resulting formulas are described and analyzed in detail.

Key words: fast automatic differentiation (FAD), Lagrangian, Euler scheme, Runge–Kutta method, splines.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:11, 1835–1859

Bibliographic databases:

UDC: 519.653
Revised: 31.05.2006

Citation: E. S. Zasukhina, “Fast automatic differentiation as applied to the computation of second derivatives of composite functions”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1923–1949; Comput. Math. Math. Phys., 46:11 (2006), 1835–1859

Citation in format AMSBIB
\Bibitem{Zas06} \by E.~S.~Zasukhina \paper Fast automatic differentiation as applied to the computation of second derivatives of composite functions \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2006 \vol 46 \issue 11 \pages 1923--1949 \mathnet{http://mi.mathnet.ru/zvmmf376} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2304067} \transl \jour Comput. Math. Math. Phys. \yr 2006 \vol 46 \issue 11 \pages 1835--1859 \crossref{https://doi.org/10.1134/S0965542506110029} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845329214}