On the choice of the function spaces for some state-constrained control problems
- 1 January 1985
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 7 (4) , 333-348
- https://doi.org/10.1080/01630568508816197
Abstract
We study a quadratic parabolic control problem with pointwise final state constraints. As the set of admissible states has an empty interior, the existence of Lagrange multipliers cannot be proved directly. We obtain, however some optimality conditions by expressing the fact that among a space of regular perturbations of the optimal control, the null perturbation is optimal. We show that the qualification hypothesis can be effectively checked in some examples and that the information given by the optimality conditions is useful because it allows to get some regularity results for the optimal control.Keywords
This publication has 2 references indexed in Scilit:
- Convex parabolic boundary control problems with pointwise state constraintsJournal of Mathematical Analysis and Applications, 1982
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinusAnnales de l'institut Fourier, 1965