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

Eduardo Casas; Fredi Tröltzsch

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 3, page 581-600
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Casas, Eduardo, and Tröltzsch, Fredi. "Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 581-600. <http://eudml.org/doc/250737>.

@article{Casas2010,
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. },
author = {Casas, Eduardo, Tröltzsch, Fredi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; pointwise state constraints; first and second order optimality conditions; Lagrange multipliers; Borel measures; optimal control},
language = {eng},
month = {7},
number = {3},
pages = {581-600},
publisher = {EDP Sciences},
title = {Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems},
url = {http://eudml.org/doc/250737},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Casas, Eduardo
AU - Tröltzsch, Fredi
TI - Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/7//
PB - EDP Sciences
VL - 16
IS - 3
SP - 581
EP - 600
AB - 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.
LA - eng
KW - Optimal control; pointwise state constraints; first and second order optimality conditions; Lagrange multipliers; Borel measures; optimal control
UR - http://eudml.org/doc/250737
ER -

References

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