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

Abstract

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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.

How to cite

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Bergounioux, 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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