Abstract
We consider the application of an SQP method to an optimal control problem governed by the heat equation with nonlinear boundary conditions. The objective functional consists of a quadratic terminal part and a quadratic regularization term. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The solution of the constrained problem is computed by solving a sequence of unconstrained ones by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behavior of the method.
This research was supported by Deutsche Forschungsgemeinschaft (DFG), under grant ”Tr 302/3-1”.
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Goldberg, H., Tröltzsch, F. (1998). On a SQP-Multigrid Technique for Nonlinear Parabolic Boundary Control Problems. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_8
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_8
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