On a SQP-multigrid technique for nonlinear parabolic boundary control problems

On a SQP-multigrid technique for nonlinear parabolic boundary control problems

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An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the proble...

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Bibliographic Details
Main Authors: Goldberg, H., Tröltzsch, F.
Language:English
Published: Technische Universität Chemnitz 1998
Subjects:
info:eu-repo/classification/ddc/510
ddc:510
optimal control
semilinear parabolic equation
multigrig method
SQP method
MSC 49M40
MSC 49M05
Online Access:http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801210
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Summary:An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method.

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