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Schiela, Anton:
State constrained optimal control problems with states of low regularity.
In: SIAM Journal on Control and Optimization.
Bd. 48
(2009)
Heft 4
.
- S. 2407-2432.
ISSN 1095-7138
DOI: https://doi.org/10.1137/080727610
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Offizieller Projekttitel Projekt-ID DFG Research Center Matheon "Mathematics for key technologies" FZT 86 |
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Deutsche Forschungsgemeinschaft |
Abstract
We consider first order optimality conditions for state constrained optimal control problems. In particular, we study the case where the state equation does not have enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.