Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints

Eduardo Casas

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 14, Issue: 3, page 575-589
  • ISSN: 1292-8119

Abstract

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The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control is Lipschitz in the whole domain. Necessary and sufficient second order conditions are proved with a minimal gap between them.

How to cite

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Casas, Eduardo. "Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2007): 575-589. <http://eudml.org/doc/90884>.

@article{Casas2007,
abstract = { The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control is Lipschitz in the whole domain. Necessary and sufficient second order conditions are proved with a minimal gap between them. },
author = {Casas, Eduardo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Elliptic control problems; pointwise state constraints; Pontryagin's principle; second order optimality conditions; elliptic control problems},
language = {eng},
month = {12},
number = {3},
pages = {575-589},
publisher = {EDP Sciences},
title = {Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints},
url = {http://eudml.org/doc/90884},
volume = {14},
year = {2007},
}

TY - JOUR
AU - Casas, Eduardo
TI - Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/12//
PB - EDP Sciences
VL - 14
IS - 3
SP - 575
EP - 589
AB - The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control is Lipschitz in the whole domain. Necessary and sufficient second order conditions are proved with a minimal gap between them.
LA - eng
KW - Elliptic control problems; pointwise state constraints; Pontryagin's principle; second order optimality conditions; elliptic control problems
UR - http://eudml.org/doc/90884
ER -

References

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