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

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

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

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topCasas, 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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