# 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

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topCasas, 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 -

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