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

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- 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 (2008): 575-589. <http://eudml.org/doc/245288>.

@article{Casas2008,

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; Pontryagin's principle},

language = {eng},

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/245288},

volume = {14},

year = {2008},

}

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

PY - 2008

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; Pontryagin's principle

UR - http://eudml.org/doc/245288

ER -

## References

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