, Volume 33, Issue 2-3, pp 209-228

Optimal Control of PDEs with Regularized Pointwise State Constraints

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Abstract

This paper addresses the regularization of pointwise state constraints in optimal control problems. By analyzing the associated dual problem, it is shown that the regularized problems admit Lagrange multipliers in L 2-spaces. Under a certain boundedness assumption, the solution of the regularized problem converges to the one of the original state constrained problem. The results of our analysis are confirmed by numerical tests.

Supported by the DFG Research Center “Mathematics for key technologies” (FZT 86) in Berlin.