New regularity results and improved error estimates for optimal control problems with state constraints

Eduardo Casas; Mariano Mateos; Boris Vexler

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 3, page 803-822
  • ISSN: 1292-8119

Abstract

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In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence for the error in L2(Ω) of the control variable is h | log h | in dimensions 2 and 3.

How to cite

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Casas, Eduardo, Mateos, Mariano, and Vexler, Boris. "New regularity results and improved error estimates for optimal control problems with state constraints." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 803-822. <http://eudml.org/doc/272945>.

@article{Casas2014,
abstract = {In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence for the error in L2(Ω) of the control variable is h | log h | in dimensions 2 and 3.},
author = {Casas, Eduardo, Mateos, Mariano, Vexler, Boris},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; state constraints; elliptic equations; Borel measures; error estimates},
language = {eng},
number = {3},
pages = {803-822},
publisher = {EDP-Sciences},
title = {New regularity results and improved error estimates for optimal control problems with state constraints},
url = {http://eudml.org/doc/272945},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Casas, Eduardo
AU - Mateos, Mariano
AU - Vexler, Boris
TI - New regularity results and improved error estimates for optimal control problems with state constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 3
SP - 803
EP - 822
AB - In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence for the error in L2(Ω) of the control variable is h | log h | in dimensions 2 and 3.
LA - eng
KW - optimal control; state constraints; elliptic equations; Borel measures; error estimates
UR - http://eudml.org/doc/272945
ER -

References

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