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.
Publié le : 2000-07-05
Classification:
Variational inequalities,
Optimal control,
Lagrange multiplier,
Obstacle problem,
AMS 49J40, 49K20, 49K35,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00022033,
author = {Bergounioux, Ma\"\i tine and Mignot, Fulbert},
title = {Optimal Control of Obstacle Problems : Existence of Lagrange Multipliers},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00022033}
}
Bergounioux, Maïtine; Mignot, Fulbert. Optimal Control of Obstacle Problems : Existence of Lagrange Multipliers. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00022033/