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Published in:
2009 | OriginalPaper | Chapter
Elliptic Control by Penalty Techniques with Control Reduction
Authors : Christian Grossmann, Holger Kunz, Robert Meischner
Published in: System Modeling and Optimization
Publisher: Springer Berlin Heidelberg
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The paper deals with the numerical treatment of optimal control problems with bounded distributed controls and elliptic state equations by a wider class of barrier-penalty methods. If the constraints are treated by barrier-penalty techniques then the necessary and sufficient optimality condition forms a coupled system of nonlinear equations which contain not only the usual adjoint and the state equation, but also an approximate projection by means of barrier-penalty terms. Under the made assumptions from the last one the control can be eliminated. This reduced optimality system which does not contain explicitly the controls, but the more regular states and adjoints only, is studied in detail.