We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear programming problems.
Publié le : 1999-07-05
Classification:
bottleneck problem,
parabolic equation,
optimal control,
pointwise state-constraint,
49K20, 90C48, 90C45,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00023012,
author = {Bergounioux, Ma\"\i tine and Tr\"oltzsch, Fredi},
title = {Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00023012}
}
Bergounioux, Maïtine; Tröltzsch, Fredi. Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00023012/