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Preprint 05-2005

On two numerical methods for state-constrained elliptic control problems

Source file is available as :   Postscript Document
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Author(s) : Christian Meyer , Uwe Pruefert , Fredi Troeltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 05-2005

MSC 2000

49J20 Optimal control problems involving partial differential equations
49M20 Methods of relaxation type

Abstract :
A linear-quadratic elliptic control problem with pointwise box constraints on the state is considered. The state-constraints are treated by a Lavrentiev type regularization. It is known that the Lagrange multipliers associated with the regularized state-constraints are functions in L^2. Moreover, the convergence of the optimal control of the regularized problem is proven for regularization parameter tending to zero. To solve the problem numerically, an interior point method and a primal-dual active set strategy are implemented and tested in function space.

Keywords : Linear elliptic equations, quadratic optimal control problem, pointwise state constraints, interior point method, active set strategy

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