The application of FAD-methodology for computing second order derivatives
by
Yu.G. Evtushenko
Computing Centre of Russian Academy of Sciences, 40, Vavilova Str., GSP-1, 117967, Moscow, Russia
Coauthors: E.S. Zasuhina (Computing Centre of Russian Academy of Sciences, Moscow, Russia), V.I. Zubov (Computing Centre of Russian Academy of Sciences, Moscow, Russia)

Unified methodology for computing second order derivatives of functions obtained in complex multistep processes is developed on the basis of general FAD approach. The formulas for Hessians arising in discretization of optimal control problems are derived. In the case of the the processes described by continuous equations we started with a arbitrary chosen discretization scheme for the governing equations and derived the exact gradient and Hessian expressions. We introduced adjoint systems for finding auxiliary vector and matrix which were used for computing the partial derivatives. A unique discretization schemes were automatically generated for vector and matrix adjoint equations. The structure of adjoint systems for some approximation schemes is found and discussed. The algebraic complexity of computing a function and its first and second derivatives is considered. Obtained formulas for second derivatives were applied for various examples which were solved before using gradient minimization methods.

http://homepages.feis.herts.ac.uk/~comqun/AD2000/Ext_Abstracts/Evtuschenko.ps

Date received: December 28, 1999