Optimal Control of PDEs with Regularized Pointwise State Constraints

Authors:
Christian Meyer;Arnd Rösch;Fredi Tröltzsch
Affiliations:
Institut für Mathematik, Technische, Universität Berlin, Berlin, Germany D-10623;Institut für Mathematik, Technische, Universität Berlin, Berlin, Germany D-10623;Institut für Mathematik, Technische, Universität Berlin, Berlin, Germany D-10623
Venue:
Computational Optimization and Applications
Year:
2006

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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 L2-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.