Publication: FAD Method to Compute Second Order Derivatives
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FAD Method to Compute Second Order Derivatives

- incollection -
 

Author(s)
Yuri G. Evtushenko , E. S. Zasuhina , V. I. Zubov

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We develop a unified methodology for computing second order derivatives of functions obtained in complex multistep processes and derive formulas for Hessians arising in discretization of optimal control problems. Where a process is described by continuous equations, we start with a discretization scheme for the state equations and derive exact gradient and Hessian expressions. We introduce adjoint systems for auxiliary vectors and matrices used for computing the derivatives. A unique discretization scheme is automatically generated for vector and matrix adjoint equations. The structure of the adjoint systems for some approximation schemes is found. The formulas for second derivatives are applied to examples.

Cross-References
Corliss2002ADo

AD Theory and Techniques
Hessian

BibTeX
@INCOLLECTION{
         Evtushenko2002FMt,
       author = "Yuri G. Evtushenko and E. S. Zasuhina and V. I. Zubov",
       title = "{FAD} Method to Compute Second Order Derivatives",
       pages = "327--333",
       chapter = "39",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "We develop a unified methodology for computing second order derivatives of
         functions obtained in complex multistep processes and derive formulas for Hessians arising in
         discretization of optimal control problems. Where a process is described by continuous equations, we
         start with a discretization scheme for the state equations and derive exact gradient and Hessian
         expressions. We introduce adjoint systems for auxiliary vectors and matrices used for computing the
         derivatives. A unique discretization scheme is automatically generated for vector and matrix adjoint
         equations. The structure of the adjoint systems for some approximation schemes is found. The
         formulas for second derivatives are applied to examples.",
       ad_theotech = "Hessian"
}


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