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