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obstacle problem.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimal Control of Obstacle Problems:Existence of LagrangeMultipliers
Maïtine Bergounioux, Fulbert Mignot
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 5 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 45-70

Print publication:

2000
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We study first order optimality systems for the control of a systemgoverned by avariationalinequality and deal with Lagrange multipliers: isit possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We givepositive and negative answers for the finite and infinite dimensional cases.These results are compared withthe previous ones got by penalization or differentiation.