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Preprint 14-2003

Optimal control of PDEs with regularized pointwise state constraints

Source file is available as :   Postscript Document

Author(s) : Christian Meyer , Arnd Roesch , Fredi Troeltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 14-2003

MSC 2000

49K20 Problems involving partial differential equations
49N10 Linear-quadratic problems
90C46 Optimality conditions, duality
49M20 Methods of relaxation type

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.

Keywords : Quadratic programming, regular Lagrange, multipliers, optimal control, elliptic and parabolic equations, pointwise state constraints, bottleneck constraints

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