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Recent advances in the analysis of pointwise state-constrainedelliptic optimal control problems

Published online by Cambridge University Press:  02 July 2009

Eduardo Casas  and
Fredi Tröltzsch
Eduardo Casas
Affiliation:
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
Fredi Tröltzsch
Affiliation:
Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany. troeltzsch@math.tu-berlin.de
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Abstract

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.

Keywords

Optimal controlpointwise state constraintsfirst and second order optimality conditionsLagrange multipliersBorel measures
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 3 , July 2010 , pp. 581 - 600
Copyright
© EDP Sciences, SMAI, 2009

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