Summary
The Newton-Picard method for the computation of time-periodic solutions of Partial Differential Equations (PDE) is an established Newton-type method. We present an improvement of the contraction rate by an overrelaxation for the Picard iteration which comes with no additional cost. Theoretical convergence results are given. Further, we extend the idea of Newton-Picard to the solution of optimization problems with time-periodic Partial Differential Equations. We discuss the resulting inexact Sequential Quadratic Programming (SQP) method and present numerical results for the ModiCon variant of the Simulated Moving Bed process.
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Acknowledgements
This work was supported by the German Research Foundation (DFG) within the priority program SPP1253 under grant BO864/12-1 and by the German Federal Ministry of Education and Research (BMBF) under grant 03BONCHD.
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Potschka, A., Küpper, A., Schlöder, J., Bock, H., Engell, S. (2010). Optimal Control of Periodic Adsorption Processes: The Newton-Picard Inexact SQP Method. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds) Recent Advances in Optimization and its Applications in Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12598-0_31
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DOI: https://doi.org/10.1007/978-3-642-12598-0_31
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