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continuous linear programming

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimal control of linear bottleneck problems
M. Bergounioux, F. Troeltzsch
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 3 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 235-250

Print publication:

1998
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The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of controltheory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-stateinequality constraints. We show how to obtain Lagrange multipliers in Lp spaces for linear problems and give an application to linearparabolic optimal control problems.