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1 Control and Cybernetics

1 2011

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Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints

Wachsmuth D., Wachsmuth G.

Control and Cybernetics

2011

Vol. 40, no 4

1125-1158

In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive a-priori regularization error estimates if the regularization parameter as well as the noise level tend to zero. We rely on an assumption that is a combination of a source condition and of a structural assumption on the active sets. Moreover, we introduce a strategy to choose the regularization parameter in dependence of the noise level. We prove convergence of this parameter choice rule with optimal order.