| Issue |
ESAIM: COCV
Volume 16, Number 3, July-September 2010
|
|
|---|---|---|
| Page(s) | 581 - 600 | |
| DOI | https://doi.org/10.1051/cocv/2009010 | |
| Published online | 02 July 2009 | |
Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
1
Dpt. Matemática Aplicada y Ciencias de la Computación,
E.T.S.I.I. y T., Universidad de Cantabria, Av. Los Castros s/n,
39005 Santander, Spain. eduardo.casas@unican.es
2
Institut für Mathematik, Technische
Universität Berlin, 10623 Berlin, Germany. troeltzsch@math.tu-berlin.de
Received:
20
July
2008
Revised:
24
February
2009
Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.
Mathematics Subject Classification: 49J20 / 49K20 / 35J65
Key words: Optimal control / pointwise state constraints / first and second order optimality conditions / Lagrange multipliers / Borel measures
© EDP Sciences, SMAI, 2009
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