Publication: Evaluating Gradients in Optimal Control: Continuous Adjoints Versus Automatic Differentiation
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Evaluating Gradients in Optimal Control: Continuous Adjoints Versus Automatic Differentiation

- Article in a journal -
 

Area
Control

Author(s)
R. Griesse , A. Walther

Published in
Journal of Optimization Theory and Applications

Year
2004

Abstract
This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator.

BibTeX
@ARTICLE{
         Griesse2004EGi,
       author = "Griesse, R. and Walther, A.",
       title = "Evaluating Gradients in Optimal Control: {C}ontinuous Adjoints Versus Automatic
         Differentiation",
       journal = "Journal of Optimization Theory and Applications",
       year = "2004",
       volume = "122",
       number = "1",
       doi = "10.1023/B:JOTA.0000041731.71309.f1",
       pages = "63--86",
       abstract = "This paper deals with the numerical solution of optimal control problems for ODEs.
         The methods considered here rely on some standard optimization code to solve a discretized version
         of the control problem under consideration. We aim to make available to the optimization software
         not only the discrete objective functional, but also its gradient. The objective gradient can be
         computed either from forward (sensitivity) information or backward (adjoint) information. The
         purpose of this paper is to discuss various ways of adjoint computation. It will be shown both
         theoretically and numerically that methods based on the continuous adjoint equation require a
         careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient
         consistent with the discretized control problem. Particular attention is given to automatic
         differentiation techniques which generate automatically a suitable integrator.",
       ad_area = "Control"
}


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