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