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2014 | OriginalPaper | Chapter

On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints

Authors : Stefanie Bott, Debora Clever, Jens Lang, Stefan Ulbrich, Jan Carsten Ziems, Dirk Schröder

Published in: Trends in PDE Constrained Optimization

Publisher: Springer International Publishing

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Abstract

We present an adaptive multilevel optimization approach which is suitable to solve complex real-world optimal control problems for time-dependent nonlinear partial differential algebraic equations with point-wise constraints on control and state. Relying on Moreau-Yosida regularization, the multilevel SQP method presented in Clever et al. (Generalized multilevel SQP-methods for PDAE-constrained optimization based on space-time adaptive PDAE solvers. In: Constrained optimization and optimal control for partial differential equations. Volume 160 of International series of numerical mathematics. Springer, Basel, pp 37–60, 2012) is extended to the state-constrained case. First-order convergence results are shown. The new multilevel SQP method is combined with the state-of-the-art software package KARDOS to allow the efficient resolution of different space and time scales in an adaptive manner. The numerical performance of the method is demonstrated and analyzed for a real-life three-dimensional radiative heat transfer problem modeling the cooling process in glass manufacturing and a two-dimensional thermistor problem modeling the heating process in steel hardening.

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previous chapter Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints
next chapter Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching
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Metadata
Title
On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints
Authors
Stefanie Bott
Debora Clever
Jens Lang
Stefan Ulbrich
Jan Carsten Ziems
Dirk Schröder
Copyright Year
2014
Book
Trends in PDE Constrained Optimization

Print ISBN: 978-3-319-05082-9

Electronic ISBN: 978-3-319-05083-6

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05083-6_7