Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

Eduardo Casas

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 8, page 345-374
  • ISSN: 1292-8119

Abstract

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The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L ∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.

How to cite

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Casas, Eduardo. "Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 345-374. <http://eudml.org/doc/244707>.

@article{Casas2002,
abstract = {The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the $L^\infty $ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.},
author = {Casas, Eduardo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {distributed control; state constraints; semilinear elliptic equation; numerical approximation; finite element method; error estimates},
language = {eng},
pages = {345-374},
publisher = {EDP-Sciences},
title = {Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints},
url = {http://eudml.org/doc/244707},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Casas, Eduardo
TI - Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
PB - EDP-Sciences
VL - 8
SP - 345
EP - 374
AB - The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the $L^\infty $ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.
LA - eng
KW - distributed control; state constraints; semilinear elliptic equation; numerical approximation; finite element method; error estimates
UR - http://eudml.org/doc/244707
ER -

References

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Citations in EuDML Documents

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  1. Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
  2. Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
  3. Pedro Merino, Fredi Tröltzsch, Boris Vexler, Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
  4. Eduardo Casas, Fredi Tröltzsch, Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
  5. Eduardo Casas, Mariano Mateos, Boris Vexler, New regularity results and improved error estimates for optimal control problems with state constraints

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