Abstract
We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.
This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1–19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Research Center, Hampton, VA 23681–0001.
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Lewis, R.M. (1998). Numerical Computation of Sensitivities and the Adjoint Approach. In: Borggaard, J., Burns, J., Cliff, E., Schreck, S. (eds) Computational Methods for Optimal Design and Control. Progress in Systems and Control Theory, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1780-0_16
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DOI: https://doi.org/10.1007/978-1-4612-1780-0_16
Publisher Name: Birkhäuser, Boston, MA
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