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W-methods in optimal control

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Abstract

This paper addresses consistency and stability of W-methods up to order three for nonlinear ODE-constrained control problems with possible restrictions on the control. The analysis is based on the transformed adjoint system and the control uniqueness property. These methods can also be applied to large-scale PDE-constrained optimization, since they offer an efficient way to compute gradients of the discrete objective function.

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Acknowledgments

J. Lang gratefully acknowledge the support of the DFG Priority Program 1253 entitled Optimization with Partial Differential Equations. We also want to thank Peter Spellucci for making his code DONLP2 available to us and for assisting us to find suitable coefficients for our ROS3WO method. I thank Jan for his long-time warm friendship and inspiring scientific collaboration. He will be greatly missed.

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Authors and Affiliations

  1. Department of Mathematics, Center of Smart Interfaces, Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 , Darmstadt, Germany

    J. Lang

  2. Center for Mathematics and Computer Science, P.O. Box 94079, 1090 GB , Amsterdam, The Netherlands

    J. G. Verwer

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  1. J. Lang
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  2. J. G. Verwer
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Correspondence to J. Lang.

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Lang, J., Verwer, J.G. W-methods in optimal control. Numer. Math. 124, 337–360 (2013). https://doi.org/10.1007/s00211-013-0516-x

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  • DOI: https://doi.org/10.1007/s00211-013-0516-x

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