# Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers

Maïtine Bergounioux; Fulbert Mignot

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 5, page 45-70
- ISSN: 1292-8119

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topBergounioux, Maïtine, and Mignot, Fulbert. "Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers ." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 45-70. <http://eudml.org/doc/116555>.

@article{Bergounioux2010,

abstract = {
We study first order optimality systems for the control of a system
governed by a variational
inequality and deal with Lagrange multipliers: is
it possible to associate to each pointwise constraint a multiplier
to get a “good” optimality system?
We give
positive and negative answers for the finite and infinite dimensional cases.
These results are compared with
the previous ones got by penalization or differentiation.
},

author = {Bergounioux, Maïtine, Mignot, Fulbert},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Variational inequalities; optimal control;
Lagrange multiplier; obstacle problem.; variational inequalities; first-order optimality systems; Lagrange multipliers},

language = {eng},

month = {3},

pages = {45-70},

publisher = {EDP Sciences},

title = {Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers },

url = {http://eudml.org/doc/116555},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Bergounioux, Maïtine

AU - Mignot, Fulbert

TI - Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 5

SP - 45

EP - 70

AB -
We study first order optimality systems for the control of a system
governed by a variational
inequality and deal with Lagrange multipliers: is
it possible to associate to each pointwise constraint a multiplier
to get a “good” optimality system?
We give
positive and negative answers for the finite and infinite dimensional cases.
These results are compared with
the previous ones got by penalization or differentiation.

LA - eng

KW - Variational inequalities; optimal control;
Lagrange multiplier; obstacle problem.; variational inequalities; first-order optimality systems; Lagrange multipliers

UR - http://eudml.org/doc/116555

ER -

## References

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